This vignette walks the core functions of the lossratio package end to end, in the order prepare the data -> fit -> diagnose -> validate -> visualise. At each step it explains what is being called, why it behaves the way it does, and how to read the result. Reading this one document is enough to grasp the full workflow.
The problem this package solves
In long-term health insurance a policy, once underwritten, stays in force for decades. The central task is therefore to look ahead and see how a group of contracts written at a given point in time (a cohort) accumulates its loss ratio as the years pass.
lossratio frames this problem on a cohort x development-period (cohort x dev) grid.
- cohort – the time a contract was underwritten (e.g. January 2023 business).
- development period (dev) – the time elapsed since underwriting.
Each cell holds a cumulative loss (loss) and a
cumulative premium (premium), and the loss ratio is defined
as ratio = loss / premium. Estimating the cells of future
development periods that have not yet been observed is the act of
projection, and the various fit_* functions in this package
perform that estimate in different ways.
The data: experience
The package ships with a synthetic experience dataset. The term experience is the domain standard, referring to the cell-level records of an actuarial experience study.
data(experience)
str(experience)
#> Classes 'data.table' and 'data.frame': 2664 obs. of 15 variables:
#> $ coverage : chr "ci" "ci" "ci" "ci" ...
#> $ uy : Date, format: "2023-01-01" "2023-01-01" ...
#> $ uy_h : Date, format: "2023-01-01" "2023-01-01" ...
#> $ uy_q : Date, format: "2023-01-01" "2023-01-01" ...
#> $ uy_m : Date, format: "2023-01-01" "2023-01-01" ...
#> $ cy : Date, format: "2023-01-01" "2023-01-01" ...
#> $ cy_h : Date, format: "2023-01-01" "2023-01-01" ...
#> $ cy_q : Date, format: "2023-01-01" "2023-01-01" ...
#> $ cy_m : Date, format: "2023-01-01" "2023-02-01" ...
#> $ dev_y : int 1 1 1 1 1 1 1 1 1 1 ...
#> $ dev_h : int 1 1 1 1 1 1 2 2 2 2 ...
#> $ dev_q : int 1 1 1 2 2 2 3 3 3 4 ...
#> $ dev_m : int 1 2 3 4 5 6 7 8 9 10 ...
#> $ incr_loss : num 1262380 11255763 11281309 33602387 7152622 ...
#> $ incr_premium: num 27993106 29183931 29401966 26570540 27471886 ...
#> - attr(*, ".internal.selfref")=<pointer: (nil)>
head(experience)
#> coverage uy uy_h uy_q uy_m cy cy_h
#> <char> <Date> <Date> <Date> <Date> <Date> <Date>
#> 1: ci 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01
#> 2: ci 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01
#> 3: ci 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01
#> 4: ci 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01
#> 5: ci 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01
#> 6: ci 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01 2023-01-01
#> cy_q cy_m dev_y dev_h dev_q dev_m incr_loss incr_premium
#> <Date> <Date> <int> <int> <int> <int> <num> <num>
#> 1: 2023-01-01 2023-01-01 1 1 1 1 1262380 27993106
#> 2: 2023-01-01 2023-02-01 1 1 1 2 11255763 29183931
#> 3: 2023-01-01 2023-03-01 1 1 1 3 11281309 29401966
#> 4: 2023-04-01 2023-04-01 1 1 2 4 33602387 26570540
#> 5: 2023-04-01 2023-05-01 1 1 2 5 7152622 27471886
#> 6: 2023-04-01 2023-06-01 1 1 2 6 10110525 26769360The key columns are:
-
coverage– the line of business (group). Four products: surgery, ci, cancer, death. -
uy_m– underwriting month. The source column for the cohort axis. -
cy_m– calendar month. -
dev_m– development month. -
incr_loss,incr_premium– incremental (per-period) loss and premium.
Note that the input is incremental: raw experience is usually accumulated in the form “how much was incurred / earned this month”. The cumulative values are constructed inside the package.
Building a Triangle – as_triangle()
as_triangle() turns raw experience into a standard
Triangle object. It performs validation, coordinate
standardisation, and aggregation in one call.
tri <- as_triangle(
experience,
groups = "coverage",
cohort = "uy_m",
calendar = "cy_m",
loss = "incr_loss",
premium = "incr_premium"
)
tri
#> shape: (2_664, 18)
#> ┌──────────┬───────────┬────────────┬───┬───────────────┬────────────────┐
#> │ coverage ┆ n_cohorts ┆ cohort ┆ … ┆ premium_share ┆ incr_premium_… │
#> │ <chr> ┆ <int> ┆ <date> ┆ … ┆ <dbl> ┆ <dbl> │
#> ├──────────┼───────────┼────────────┼───┼───────────────┼────────────────┤
#> │ ci ┆ 36 ┆ 2023-01-01 ┆ … ┆ 0.381171 ┆ 0.381171 │
#> │ ci ┆ 35 ┆ 2023-01-01 ┆ … ┆ 0.380346 ┆ 0.379558 │
#> │ ci ┆ 34 ┆ 2023-01-01 ┆ … ┆ 0.387352 ┆ 0.401744 │
#> │ ci ┆ 33 ┆ 2023-01-01 ┆ … ┆ 0.379535 ┆ 0.356118 │
#> │ ci ┆ 32 ┆ 2023-01-01 ┆ … ┆ 0.377646 ┆ 0.370060 │
#> │ … ┆ … ┆ … ┆ … ┆ … ┆ … │
#> │ surgery ┆ 35 ┆ 2025-10-01 ┆ … ┆ 0.872357 ┆ 0.874228 │
#> │ surgery ┆ 34 ┆ 2025-10-01 ┆ … ┆ 0.874537 ┆ 0.878680 │
#> │ surgery ┆ 36 ┆ 2025-11-01 ┆ … ┆ 0.667521 ┆ 0.667521 │
#> │ surgery ┆ 35 ┆ 2025-11-01 ┆ … ┆ 0.669140 ┆ 0.670648 │
#> │ surgery ┆ 36 ┆ 2025-12-01 ┆ … ┆ 0.544008 ┆ 0.544008 │
#> └──────────┴───────────┴────────────┴───┴───────────────┴────────────────┘
#> 13 more variables: dev <int>, loss <dbl>, incr_loss <dbl>, premium <dbl>,
#> incr_premium <dbl>, ratio <dbl>, incr_ratio <dbl>,
#> margin <dbl>, incr_margin <dbl>, profit <fct>,
#> incr_profit <fct>, loss_share <dbl>, incr_loss_share <dbl>It takes the original column names (uy_m,
incr_loss, …) and renames them to standard names
(cohort, dev, loss,
premium, …), preserving the originals as attributes. The
output columns are cumulative by default, with
incremental columns carrying the incr_ prefix –
loss/incr_loss,
premium/incr_premium,
ratio/incr_ratio.
If you already hold a cumulative triangle, pass
cell_type = "cumulative". as_triangle() then
differences within each cohort to recover the increments
automatically.
# when loss / premium are already cumulative
as_triangle(df_cumulative,
groups = "coverage", cohort = "uy_m", calendar = "cy_m",
loss = "loss", premium = "premium",
cell_type = "cumulative")The rest of the walkthrough uses a single product so the output stays compact.
tri1 <- as_triangle(
experience[coverage == "surgery"],
groups = "coverage",
cohort = "uy_m",
calendar = "cy_m",
loss = "incr_loss",
premium = "incr_premium"
)The triangle itself can be viewed as a heatmap.
plot_triangle(tri1, metric = "ratio")
Only the upper-left region (the observed area) is filled; the empty lower-right cells are the future cells still to be projected.
Two views of loss development
To project future cells, the way “loss grows over development time” must be expressed as a model. lossratio uses two basic views.
-
Multiplicative – chain ladder (CL). The cumulative
loss at the next development period is a multiple of the current one:
C_{k+1} = f_k * C_k. Heref_kis the age-to-age factor, estimated as the ratio of cumulative loss between two adjacent development periods. -
Additive – exposure-driven (ED). The loss
increment of the next period is made proportional to premium:
Δloss = g_k * premium.g_kis the loss intensity per unit of premium.
The two are complementary. Early in development the cumulative loss is small, so the age-to-age factor swings widely; anchoring on premium makes the exposure-driven view more stable. As development matures the age-to-age factor settles, and chain ladder preserves the cohort’s own observed level well.
fit_cl() – chain ladder
fit_cl() performs a Mack (1993) chain ladder fit on the
cumulative loss.
cl <- fit_cl(tri1)
summary(cl)
#> coverage cohort latest loss_ult reserve loss_proc_se
#> <char> <Date> <num> <num> <num> <num>
#> 1: surgery 2023-01-01 410248522 410248522 0 0
#> 2: surgery 2023-02-01 976330445 1001441303 25110858 2751819
#> 3: surgery 2023-03-01 978486045 1026151243 47665198 3967869
#> 4: surgery 2023-04-01 2029909919 2186771221 156861302 6942937
#> 5: surgery 2023-05-01 624219436 697669301 73449865 4455636
#> 6: surgery 2023-06-01 802880717 931393934 128513217 17869565
#> 7: surgery 2023-07-01 2539141549 3050990158 511848609 35918003
#> 8: surgery 2023-08-01 393678329 488218204 94539875 15583801
#> 9: surgery 2023-09-01 1364052542 1751869308 387816766 38001618
#> 10: surgery 2023-10-01 979266043 1311793843 332527800 38496097
#> 11: surgery 2023-11-01 604685679 848103123 243417444 35719579
#> 12: surgery 2023-12-01 1026345366 1497869029 471523663 51405333
#> 13: surgery 2024-01-01 1912177598 2901492851 989315253 75674312
#> 14: surgery 2024-02-01 733902485 1160045952 426143467 51719398
#> 15: surgery 2024-03-01 415459873 686574148 271114275 41313266
#> 16: surgery 2024-04-01 3286053526 5687484014 2401430488 122770258
#> 17: surgery 2024-05-01 1451731153 2645801838 1194070685 93024106
#> 18: surgery 2024-06-01 629668308 1209024555 579356247 65346187
#> 19: surgery 2024-07-01 1250954693 2542927190 1291972497 103136528
#> 20: surgery 2024-08-01 425346694 918120582 492773888 65317866
#> 21: surgery 2024-09-01 278156543 635470028 357313485 56737053
#> 22: surgery 2024-10-01 352070323 856446521 504376198 68091257
#> 23: surgery 2024-11-01 99050501 260916096 161865595 41787166
#> 24: surgery 2024-12-01 103194013 295637296 192443283 49617195
#> 25: surgery 2025-01-01 227089025 710560093 483471068 83635489
#> 26: surgery 2025-02-01 939163074 3276849152 2337686078 192418633
#> 27: surgery 2025-03-01 112828845 434950057 322121212 72345359
#> 28: surgery 2025-04-01 82472453 356301148 273828695 68974257
#> 29: surgery 2025-05-01 141214851 697290587 556075736 119238986
#> 30: surgery 2025-06-01 136406102 789468799 653062697 136628652
#> 31: surgery 2025-07-01 149144024 1040451732 891307708 167039609
#> 32: surgery 2025-08-01 116327076 1008356733 892029657 183653360
#> 33: surgery 2025-09-01 67465470 783000257 715534787 179947037
#> 34: surgery 2025-10-01 121626173 2001214863 1879588690 337103186
#> 35: surgery 2025-11-01 15716444 449653406 433936962 194100658
#> 36: surgery 2025-12-01 4825085 850839118 846014033 472741759
#> coverage cohort latest loss_ult reserve loss_proc_se
#> <char> <Date> <num> <num> <num> <num>
#> loss_param_se loss_total_se loss_total_cv
#> <num> <num> <num>
#> 1: 0 0 0.000000000
#> 2: 4299412 5104650 0.005097304
#> 3: 5021196 6399718 0.006236623
#> 4: 11297887 13260717 0.006064062
#> 5: 3696918 5789637 0.008298541
#> 6: 8694892 19872657 0.021336469
#> 7: 30501066 47121311 0.015444596
#> 8: 5072721 16388635 0.033568259
#> 9: 20827314 43334744 0.024736288
#> 10: 16992221 42079509 0.032077837
#> 11: 11901733 37650227 0.044393454
#> 12: 22008504 55918535 0.037332059
#> 13: 43971810 87522121 0.030164514
#> 14: 18269127 54851227 0.047283667
#> 15: 11014493 42756344 0.062274911
#> 16: 92689755 153830838 0.027047256
#> 17: 45040851 103354548 0.039063601
#> 18: 20907249 68609309 0.056747655
#> 19: 45568404 112754702 0.044340515
#> 20: 16819267 67448584 0.073463753
#> 21: 11859688 57963310 0.091213288
#> 22: 16219631 69996398 0.081728860
#> 23: 5190764 42108328 0.161386470
#> 24: 6221683 50005754 0.169145620
#> 25: 15668260 85090478 0.119751276
#> 26: 75222224 206599403 0.063048188
#> 27: 10161412 73055495 0.167962950
#> 28: 8575343 69505285 0.195074548
#> 29: 19174475 120770842 0.173200161
#> 30: 22834478 138523651 0.175464377
#> 31: 31445935 169973756 0.163365345
#> 32: 32987225 186592373 0.185045993
#> 33: 27713231 182068556 0.232526816
#> 34: 80113491 346492034 0.173140846
#> 35: 21034520 195237078 0.434194593
#> 36: 66075497 477337136 0.561019265
#> loss_param_se loss_total_se loss_total_cv
#> <num> <num> <num>summary() reports the ultimate loss per cohort with its
standard error (loss_total_se) and coefficient of variation
(loss_total_cv). The standard error follows Mack’s variance
decomposition, computed as the sum of process error and
parameter error.
The $full slot holds the cell-level result over both the
observed and projected regions.
head(cl$full[, c("cohort", "dev", "loss_obs", "loss_proj",
"loss_total_se", "is_observed")])
#> cohort dev loss_obs loss_proj loss_total_se is_observed
#> <Date> <int> <num> <num> <num> <lgcl>
#> 1: 2023-01-01 1 1886123 1886123 0 TRUE
#> 2: 2023-01-01 2 14030514 14030514 0 TRUE
#> 3: 2023-01-01 3 24427715 24427715 0 TRUE
#> 4: 2023-01-01 4 34672477 34672477 0 TRUE
#> 5: 2023-01-01 5 44990229 44990229 0 TRUE
#> 6: 2023-01-01 6 55621697 55621697 0 TRUEThe projection curves connect each cohort’s observed values (solid) with its projection (dashed).
plot(cl)
fit_ed() – exposure-driven
fit_ed() fits the same triangle with the additive
exposure-driven model.
ed <- fit_ed(tri1)
summary(ed)
#> Key: <coverage>
#> coverage ata_from ata_to ata_link mean median wt cv g
#> <char> <num> <num> <fctr> <num> <num> <num> <num> <num>
#> 1: surgery 1 2 1-2 1.34661 1.21766 1.31614 0.47327 1.31614
#> 2: surgery 2 3 2-3 0.58109 0.56432 0.58674 0.37381 0.58674
#> 3: surgery 3 4 3-4 0.39105 0.36751 0.38178 0.43535 0.38178
#> 4: surgery 4 5 4-5 0.31110 0.32321 0.33127 0.35969 0.33127
#> 5: surgery 5 6 5-6 0.27543 0.25088 0.25518 0.43531 0.25518
#> 6: surgery 6 7 6-7 0.21364 0.20479 0.22393 0.31371 0.22393
#> 7: surgery 7 8 7-8 0.18072 0.18227 0.19476 0.36392 0.19476
#> 8: surgery 8 9 8-9 0.16798 0.15484 0.16849 0.67814 0.16849
#> 9: surgery 9 10 9-10 0.14955 0.13195 0.14572 0.33906 0.14572
#> 10: surgery 10 11 10-11 0.12550 0.12095 0.12851 0.31241 0.12851
#> 11: surgery 11 12 11-12 0.13833 0.12898 0.14581 0.39551 0.14581
#> 12: surgery 12 13 12-13 0.12519 0.11356 0.12075 0.34186 0.12075
#> 13: surgery 13 14 13-14 0.11144 0.10927 0.11631 0.35239 0.11631
#> 14: surgery 14 15 14-15 0.10561 0.09421 0.11169 0.43662 0.11169
#> 15: surgery 15 16 15-16 0.08954 0.08726 0.08964 0.34359 0.08964
#> 16: surgery 16 17 16-17 0.08079 0.07993 0.08162 0.24700 0.08162
#> 17: surgery 17 18 17-18 0.08109 0.07612 0.08725 0.28780 0.08725
#> 18: surgery 18 19 18-19 0.08636 0.08620 0.08772 0.34300 0.08772
#> 19: surgery 19 20 19-20 0.07944 0.07838 0.08008 0.25109 0.08008
#> 20: surgery 20 21 20-21 0.07789 0.07935 0.08007 0.32197 0.08007
#> 21: surgery 21 22 21-22 0.06746 0.06606 0.06982 0.26290 0.06982
#> 22: surgery 22 23 22-23 0.06748 0.06394 0.06703 0.32299 0.06703
#> 23: surgery 23 24 23-24 0.06644 0.05971 0.06165 0.39463 0.06165
#> 24: surgery 24 25 24-25 0.06303 0.05711 0.05902 0.45911 0.05902
#> 25: surgery 25 26 25-26 0.06696 0.06136 0.06056 0.39347 0.06056
#> 26: surgery 26 27 26-27 0.06265 0.05387 0.07093 0.44081 0.07093
#> 27: surgery 27 28 27-28 0.06010 0.05136 0.06550 0.36862 0.06550
#> 28: surgery 28 29 28-29 0.06012 0.06544 0.05404 0.31348 0.05404
#> 29: surgery 29 30 29-30 0.05275 0.04745 0.04877 0.23587 0.04877
#> 30: surgery 30 31 30-31 0.05437 0.04834 0.05359 0.25583 0.05359
#> 31: surgery 31 32 31-32 0.06003 0.05618 0.05643 0.41162 0.05643
#> 32: surgery 32 33 32-33 0.05749 0.05671 0.05622 0.07265 0.05622
#> 33: surgery 33 34 33-34 0.04049 0.03873 0.04100 0.08481 0.04100
#> 34: surgery 34 35 34-35 0.03562 0.03562 0.03403 0.15183 0.03403
#> 35: surgery 35 36 35-36 0.03864 0.03864 0.03864 NA 0.03864
#> coverage ata_from ata_to ata_link mean median wt cv g
#> <char> <num> <num> <fctr> <num> <num> <num> <num> <num>
#> g_se rse sigma n_cohorts n_valid n_inf n_nan valid_ratio
#> <num> <num> <num> <num> <num> <num> <num> <num>
#> 1: 0.09107 0.06919 2930.74379 35 35 0 0 1
#> 2: 0.03508 0.05979 1580.26206 34 34 0 0 1
#> 3: 0.02931 0.07677 1587.18687 33 33 0 0 1
#> 4: 0.02135 0.06444 1319.11056 32 32 0 0 1
#> 5: 0.02087 0.08178 1421.47805 31 31 0 0 1
#> 6: 0.01273 0.05686 937.78642 30 30 0 0 1
#> 7: 0.01141 0.05860 897.25756 29 29 0 0 1
#> 8: 0.02169 0.12870 1792.82291 28 28 0 0 1
#> 9: 0.00943 0.06471 819.85457 27 27 0 0 1
#> 10: 0.00676 0.05263 614.41506 26 26 0 0 1
#> 11: 0.01185 0.08130 1065.55644 25 25 0 0 1
#> 12: 0.00987 0.08170 911.69544 24 24 0 0 1
#> 13: 0.01111 0.09556 1061.51299 23 23 0 0 1
#> 14: 0.01140 0.10209 1123.12989 22 22 0 0 1
#> 15: 0.00630 0.07031 629.63157 21 21 0 0 1
#> 16: 0.00475 0.05825 483.04483 20 20 0 0 1
#> 17: 0.00628 0.07198 644.16296 19 19 0 0 1
#> 18: 0.00745 0.08497 734.39263 18 18 0 0 1
#> 19: 0.00438 0.05473 434.93473 17 17 0 0 1
#> 20: 0.00692 0.08645 667.93909 16 16 0 0 1
#> 21: 0.00444 0.06361 392.59516 15 15 0 0 1
#> 22: 0.00501 0.07472 445.50689 14 14 0 0 1
#> 23: 0.00644 0.10443 566.66986 13 13 0 0 1
#> 24: 0.00532 0.09006 436.45244 12 12 0 0 1
#> 25: 0.00638 0.10534 505.82971 11 11 0 0 1
#> 26: 0.00878 0.12380 684.49354 10 10 0 0 1
#> 27: 0.00834 0.12727 627.18471 9 9 0 0 1
#> 28: 0.00853 0.15779 604.48158 8 8 0 0 1
#> 29: 0.00428 0.08784 300.99607 7 7 0 0 1
#> 30: 0.00553 0.10315 325.88934 6 6 0 0 1
#> 31: 0.01155 0.20459 641.18962 5 5 0 0 1
#> 32: 0.00153 0.02721 80.36415 4 4 0 0 1
#> 33: 0.00211 0.05148 81.83368 3 3 0 0 1
#> 34: 0.00348 0.10217 103.52601 2 2 0 0 1
#> 35: NA NA NA 1 1 0 0 1
#> g_se rse sigma n_cohorts n_valid n_inf n_nan valid_ratio
#> <num> <num> <num> <num> <num> <num> <num> <num>The point projection (loss_proj) is nearly identical
between chain ladder and exposure-driven – both explain the same data.
The difference lies in how the variance accumulates. Chain
ladder amplifies variance through the square of the multiplier
f, while the exposure-driven model adds
premium-proportional increments. As a result the exposure-driven
standard error is calmer in the early development periods.
fit_sa() – stage-adaptive
fit_sa() blends the two views in a stage-adaptive (SA)
way: the development periods before the maturity point are fit with the
exposure-driven model, and the periods after it with chain ladder.
sa <- fit_sa(tri1)
summary(sa)
#> coverage cohort loss_ult loss_total_se loss_total_cv
#> <char> <Date> <num> <num> <num>
#> 1: surgery 2023-01-01 410248522 0 0.000000000
#> 2: surgery 2023-02-01 1001441303 5213830 0.005206903
#> 3: surgery 2023-03-01 1026151243 6516765 0.006351412
#> 4: surgery 2023-04-01 2186771221 13328275 0.006095671
#> 5: surgery 2023-05-01 697669301 5934623 0.008507146
#> 6: surgery 2023-06-01 931393934 19748953 0.021210955
#> 7: surgery 2023-07-01 3050990158 47562095 0.015597747
#> 8: surgery 2023-08-01 488218204 16944542 0.034721030
#> 9: surgery 2023-09-01 1751869308 42574746 0.024314556
#> 10: surgery 2023-10-01 1311793843 41329107 0.031518532
#> 11: surgery 2023-11-01 848103123 37157863 0.043825274
#> 12: surgery 2023-12-01 1497869029 57599154 0.038467355
#> 13: surgery 2024-01-01 2901492851 88235644 0.030420598
#> 14: surgery 2024-02-01 1160045952 54795036 0.047259587
#> 15: surgery 2024-03-01 686574148 43001505 0.062669337
#> 16: surgery 2024-04-01 5687484014 153573839 0.027023203
#> 17: surgery 2024-05-01 2645801838 99819176 0.037767381
#> 18: surgery 2024-06-01 1209024555 70198966 0.058126448
#> 19: surgery 2024-07-01 2542927190 113847340 0.044828055
#> 20: surgery 2024-08-01 918120582 65147845 0.071058089
#> 21: surgery 2024-09-01 635470028 57830189 0.091140754
#> 22: surgery 2024-10-01 856446521 72983751 0.085349352
#> 23: surgery 2024-11-01 260916096 41722607 0.160138402
#> 24: surgery 2024-12-01 295637296 49055982 0.166160578
#> 25: surgery 2025-01-01 710560093 84025806 0.118458337
#> 26: surgery 2025-02-01 3276849152 207578746 0.063455505
#> 27: surgery 2025-03-01 434950057 72002829 0.165840618
#> 28: surgery 2025-04-01 356301148 69341707 0.194927969
#> 29: surgery 2025-05-01 697290587 118074803 0.169587982
#> 30: surgery 2025-06-01 789468799 138920305 0.176211772
#> 31: surgery 2025-07-01 1040451732 169134660 0.162761021
#> 32: surgery 2025-08-01 1008356733 187372862 0.185979990
#> 33: surgery 2025-09-01 783000257 182485783 0.233248980
#> 34: surgery 2025-10-01 2001214863 340964049 0.170558023
#> 35: surgery 2025-11-01 576954661 191871774 0.427367699
#> 36: surgery 2025-12-01 1246569307 468598419 0.551014826
#> coverage cohort loss_ult loss_total_se loss_total_cv
#> <char> <Date> <num> <num> <num>The maturity point is the development period where the age-to-age factor has settled sufficiently, detected automatically inside the fit (two-pass). The intuition is simple: the early region, where the age-to-age factor still swings, anchors on premium (ED); the settled region thereafter follows the cohort’s own development (CL). Stage adaptation is the package’s default workhorse for long-term loss-ratio projection.
plot(sa)
fit_bf() – Bornhuetter-Ferguson
fit_bf() brings in an external prior loss
ratio. The portion of loss that has not yet emerged is filled
not by the data but by the prior.
q_i is the emergence ratio of cohort i
(L^{obs} / L^{ult, CL}). In other words
Bornhuetter-Ferguson is a credibility blend that fills the
already-emerged part with data and the not-yet-emerged part
with the prior. The prior argument is required.
bf <- fit_bf(tri1, prior = 0.70)
summary(bf)
#> coverage cohort latest loss_ult reserve elr q
#> <char> <Date> <num> <num> <num> <num> <num>
#> 1: surgery 2023-01-01 410248522 410248522 0 0.7 1.000000000
#> 2: surgery 2023-02-01 976330445 988014446 11684001 0.7 0.974925282
#> 3: surgery 2023-03-01 978486045 1001313340 22827295 0.7 0.953549540
#> 4: surgery 2023-04-01 2029909919 2103440848 73530929 0.7 0.928268078
#> 5: surgery 2023-05-01 624219436 659825088 35605652 0.7 0.894721088
#> 6: surgery 2023-06-01 802880717 860017751 57137034 0.7 0.862020556
#> 7: surgery 2023-07-01 2539141549 2769110891 229969342 0.7 0.832235247
#> 8: surgery 2023-08-01 393678329 438075731 44397402 0.7 0.806357333
#> 9: surgery 2023-09-01 1364052542 1533228915 169176373 0.7 0.778626885
#> 10: surgery 2023-10-01 979266043 1132613702 153347659 0.7 0.746509101
#> 11: surgery 2023-11-01 604685679 731321345 126635666 0.7 0.712986030
#> 12: surgery 2023-12-01 1026345366 1259276578 232931212 0.7 0.685203677
#> 13: surgery 2024-01-01 1912177598 2391691252 479513654 0.7 0.659032331
#> 14: surgery 2024-02-01 733902485 947906510 214004025 0.7 0.632649494
#> 15: surgery 2024-03-01 415459873 541048315 125588442 0.7 0.605120181
#> 16: surgery 2024-04-01 3286053526 4282833085 996779559 0.7 0.577769277
#> 17: surgery 2024-05-01 1451731153 2051922702 600191549 0.7 0.548692322
#> 18: surgery 2024-06-01 629668308 881286702 251618394 0.7 0.520806882
#> 19: surgery 2024-07-01 1250954693 2279320912 1028366219 0.7 0.491934924
#> 20: surgery 2024-08-01 425346694 792385329 367038635 0.7 0.463279772
#> 21: surgery 2024-09-01 278156543 555212439 277055896 0.7 0.437717801
#> 22: surgery 2024-10-01 352070323 758060195 405989872 0.7 0.411082670
#> 23: surgery 2024-11-01 99050501 239786684 140736183 0.7 0.379625874
#> 24: surgery 2024-12-01 103194013 270168423 166974410 0.7 0.349056139
#> 25: surgery 2025-01-01 227089025 624183994 397094969 0.7 0.319591583
#> 26: surgery 2025-02-01 939163074 2580188625 1641025551 0.7 0.286605526
#> 27: surgery 2025-03-01 112828845 406416040 293587195 0.7 0.259406438
#> 28: surgery 2025-04-01 82472453 338988233 256515780 0.7 0.231468390
#> 29: surgery 2025-05-01 141214851 714552172 573337321 0.7 0.202519371
#> 30: surgery 2025-06-01 136406102 589825915 453419813 0.7 0.172782132
#> 31: surgery 2025-07-01 149144024 664688641 515544617 0.7 0.143345452
#> 32: surgery 2025-08-01 116327076 758604071 642276995 0.7 0.115363018
#> 33: surgery 2025-09-01 67465470 458478144 391012674 0.7 0.086162769
#> 34: surgery 2025-10-01 121626173 1001607436 879981263 0.7 0.060776169
#> 35: surgery 2025-11-01 15716444 416407427 400690983 0.7 0.034952352
#> 36: surgery 2025-12-01 4825085 716557798 711732713 0.7 0.005670972
#> coverage cohort latest loss_ult reserve elr q
#> <char> <Date> <num> <num> <num> <num> <num>
#> loss_total_se loss_total_cv loss_ci_lo loss_ci_hi
#> <num> <num> <num> <num>
#> 1: 0 0.000000000 410248522 410248522
#> 2: 2706900 0.002739737 982709020 993319872
#> 3: 3577408 0.003572716 994301749 1008324932
#> 4: 6838847 0.003251267 2090036953 2116844742
#> 5: 3492508 0.005293082 652979898 666670278
#> 6: 12372795 0.014386674 835767517 884267984
#> 7: 26644265 0.009621956 2716889092 2821332690
#> 8: 10853531 0.024775468 416803200 459348261
#> 9: 26083909 0.017012404 1482105392 1584352438
#> 10: 26797039 0.023659469 1080092472 1185134933
#> 11: 26147262 0.035753452 680073652 782569037
#> 12: 36904052 0.029305756 1186945964 1331607192
#> 13: 54554640 0.022810068 2284766123 2498616381
#> 14: 37132355 0.039173014 875128432 1020684589
#> 15: 28309725 0.052323840 485562273 596534358
#> 16: 82259622 0.019206824 4121607187 4444058982
#> 17: 67184067 0.032742007 1920244351 2183601052
#> 18: 43376322 0.049219309 796270672 966302731
#> 19: 93872014 0.041184202 2095335146 2463306678
#> 20: 56754159 0.071624444 681149222 903621437
#> 21: 50204160 0.090423334 456814094 653610784
#> 22: 61451372 0.081063974 637617720 878502671
#> 23: 39077740 0.162968764 163195722 316377647
#> 24: 46347332 0.171549773 179329323 361007524
#> 25: 76064334 0.121862039 475100639 773267350
#> 26: 162339147 0.062917550 2262009743 2898367507
#> 27: 69290105 0.170490578 270609928 542222151
#> 28: 66987095 0.197608910 207695939 470280527
#> 29: 121492740 0.170026409 476430778 952673567
#> 30: 114220772 0.193651668 365957315 813694515
#> 31: 127500326 0.191819625 414792595 914584687
#> 32: 156435540 0.206215002 451996047 1065212095
#> 33: 133546948 0.291283127 196730936 720225351
#> 34: 231723393 0.231351511 547437930 1455776941
#> 35: 187300253 0.449800461 49305677 783509176
#> 36: 434845529 0.606853390 -135723778 1568839373
#> loss_total_se loss_total_cv loss_ci_lo loss_ci_hi
#> <num> <num> <num> <num>The prior can vary by cohort (a data frame) or be a distributional
prior (with an elr_se column). The younger a cohort – the
less data it has – the more its result is pulled toward the prior; that
is precisely the reason to use Bornhuetter-Ferguson.
fit_cc() – Cape Cod
fit_cc() has the same structure as Bornhuetter-Ferguson,
except the prior loss ratio is not supplied externally – it is
estimated by pooling the data.
cc <- fit_cc(tri1)
summary(cc)
#> coverage cohort latest loss_ult reserve elr q
#> <char> <Date> <num> <num> <num> <num> <num>
#> 1: surgery 2023-01-01 410248522 410248522 0 1.355821 1.000000000
#> 2: surgery 2023-02-01 976330445 998961036 22630591 1.355821 0.974925282
#> 3: surgery 2023-03-01 978486045 1022699937 44213892 1.355821 0.953549540
#> 4: surgery 2023-04-01 2029909919 2172331022 142421103 1.355821 0.928268078
#> 5: surgery 2023-05-01 624219436 693183562 68964126 1.355821 0.894721088
#> 6: surgery 2023-06-01 802880717 913548697 110667980 1.355821 0.862020556
#> 7: surgery 2023-07-01 2539141549 2984566188 445424639 1.355821 0.832235247
#> 8: surgery 2023-08-01 393678329 479671081 85992752 1.355821 0.806357333
#> 9: surgery 2023-09-01 1364052542 1691728066 327675524 1.355821 0.778626885
#> 10: surgery 2023-10-01 979266043 1276283138 297017095 1.355821 0.746509101
#> 11: surgery 2023-11-01 604685679 849964659 245278980 1.355821 0.712986030
#> 12: surgery 2023-12-01 1026345366 1477506812 451161446 1.355821 0.685203677
#> 13: surgery 2024-01-01 1912177598 2840941382 928763784 1.355821 0.659032331
#> 14: surgery 2024-02-01 733902485 1148404108 414501623 1.355821 0.632649494
#> 15: surgery 2024-03-01 415459873 658710499 243250626 1.355821 0.605120181
#> 16: surgery 2024-04-01 3286053526 5216702938 1930649412 1.355821 0.577769277
#> 17: surgery 2024-05-01 1451731153 2614234387 1162503234 1.355821 0.548692322
#> 18: surgery 2024-06-01 629668308 1117024715 487356407 1.355821 0.520806882
#> 19: surgery 2024-07-01 1250954693 3242783898 1991829205 1.355821 0.491934924
#> 20: surgery 2024-08-01 425346694 1136259071 710912377 1.355821 0.463279772
#> 21: surgery 2024-09-01 278156543 814782518 536625975 1.355821 0.437717801
#> 22: surgery 2024-10-01 352070323 1138426847 786356524 1.355821 0.411082670
#> 23: surgery 2024-11-01 99050501 371640591 272590090 1.355821 0.379625874
#> 24: surgery 2024-12-01 103194013 426604585 323410572 1.355821 0.349056139
#> 25: surgery 2025-01-01 227089025 996217126 769128101 1.355821 0.319591583
#> 26: surgery 2025-02-01 939163074 4117644201 3178481127 1.355821 0.286605526
#> 27: surgery 2025-03-01 112828845 681474078 568645233 1.355821 0.259406438
#> 28: surgery 2025-04-01 82472453 579314544 496842091 1.355821 0.231468390
#> 29: surgery 2025-05-01 141214851 1251704480 1110489629 1.355821 0.202519371
#> 30: surgery 2025-06-01 136406102 1014629063 878222961 1.355821 0.172782132
#> 31: surgery 2025-07-01 149144024 1147695713 998551689 1.355821 0.143345452
#> 32: surgery 2025-08-01 116327076 1360345066 1244017990 1.355821 0.115363018
#> 33: surgery 2025-09-01 67465470 824812852 757347382 1.355821 0.086162769
#> 34: surgery 2025-10-01 121626173 1826050478 1704424305 1.355821 0.060776169
#> 35: surgery 2025-11-01 15716444 791809616 776093172 1.355821 0.034952352
#> 36: surgery 2025-12-01 4825085 1383370954 1378545869 1.355821 0.005670972
#> coverage cohort latest loss_ult reserve elr q
#> <char> <Date> <num> <num> <num> <num> <num>
#> loss_total_se loss_total_cv loss_ci_lo loss_ci_hi elr_cc_se elr_cc_cv
#> <num> <num> <num> <num> <num> <num>
#> 1: 0 0.000000000 410248522 410248522 0.004723362 0.003483765
#> 2: 4593602 0.004598379 989957742 1007964329 0.004723362 0.003483765
#> 3: 5861160 0.005731065 1011212275 1034187600 0.004723362 0.003483765
#> 4: 11606085 0.005342687 2149583513 2195078531 0.004723362 0.003483765
#> 5: 5324825 0.007681696 682747097 703620028 0.004723362 0.003483765
#> 6: 17799733 0.019484165 878661861 948435533 0.004723362 0.003483765
#> 7: 40172904 0.013460215 2905828743 3063303632 0.004723362 0.003483765
#> 8: 15331659 0.031962858 449621582 509720580 0.004723362 0.003483765
#> 9: 37557573 0.022200715 1618116576 1765339557 0.004723362 0.003483765
#> 10: 38142195 0.029885371 1201525810 1351040465 0.004723362 0.003483765
#> 11: 36892692 0.043404972 777656311 922273007 0.004723362 0.003483765
#> 12: 52372680 0.035446659 1374858246 1580155378 0.004723362 0.003483765
#> 13: 78351886 0.027579550 2687374507 2994508257 0.004723362 0.003483765
#> 14: 52317595 0.045556781 1045863507 1250944710 0.004723362 0.003483765
#> 15: 39656345 0.060202995 580985491 736435508 0.004723362 0.003483765
#> 16: 118649233 0.022744104 4984154715 5449251161 0.004723362 0.003483765
#> 17: 95166627 0.036403250 2427711225 2800757549 0.004723362 0.003483765
#> 18: 60795329 0.054426127 997868060 1236181369 0.004723362 0.003483765
#> 19: 133200048 0.041075832 2981716601 3503851194 0.004723362 0.003483765
#> 20: 79519501 0.069983601 980403712 1292114430 0.004723362 0.003483765
#> 21: 70211447 0.086172009 677170611 952394425 0.004723362 0.003483765
#> 22: 86035035 0.075573618 969801276 1307052417 0.004723362 0.003483765
#> 23: 54540884 0.146757070 264742423 478538760 0.004723362 0.003483765
#> 24: 64681286 0.151618825 299831594 553377576 0.004723362 0.003483765
#> 25: 106241396 0.106644820 787987815 1204446437 0.004723362 0.003483765
#> 26: 227653283 0.055287264 3671451966 4563836436 0.004723362 0.003483765
#> 27: 96742990 0.141961364 491861302 871086855 0.004723362 0.003483765
#> 28: 93540835 0.161468129 395977876 762651212 0.004723362 0.003483765
#> 29: 169670289 0.135551395 919156825 1584252135 0.004723362 0.003483765
#> 30: 159480991 0.157181572 702052063 1327206062 0.004723362 0.003483765
#> 31: 178077636 0.155161019 798669960 1496721466 0.004723362 0.003483765
#> 32: 218535228 0.160646908 932023889 1788666243 0.004723362 0.003483765
#> 33: 186560125 0.226184794 459161726 1190463978 0.004723362 0.003483765
#> 34: 323931990 0.177394871 1191155445 2460945512 0.004723362 0.003483765
#> 35: 261700792 0.330509742 278885490 1304733743 0.004723362 0.003483765
#> 36: 606816525 0.438650619 194032420 2572709489 0.004723362 0.003483765
#> loss_total_se loss_total_cv loss_ci_lo loss_ci_hi elr_cc_se elr_cc_cv
#> <num> <num> <num> <num> <num> <num>
#> elr_cc_ci_lo elr_cc_ci_hi
#> <num> <num>
#> 1: 1.346563 1.365079
#> 2: 1.346563 1.365079
#> 3: 1.346563 1.365079
#> 4: 1.346563 1.365079
#> 5: 1.346563 1.365079
#> 6: 1.346563 1.365079
#> 7: 1.346563 1.365079
#> 8: 1.346563 1.365079
#> 9: 1.346563 1.365079
#> 10: 1.346563 1.365079
#> 11: 1.346563 1.365079
#> 12: 1.346563 1.365079
#> 13: 1.346563 1.365079
#> 14: 1.346563 1.365079
#> 15: 1.346563 1.365079
#> 16: 1.346563 1.365079
#> 17: 1.346563 1.365079
#> 18: 1.346563 1.365079
#> 19: 1.346563 1.365079
#> 20: 1.346563 1.365079
#> 21: 1.346563 1.365079
#> 22: 1.346563 1.365079
#> 23: 1.346563 1.365079
#> 24: 1.346563 1.365079
#> 25: 1.346563 1.365079
#> 26: 1.346563 1.365079
#> 27: 1.346563 1.365079
#> 28: 1.346563 1.365079
#> 29: 1.346563 1.365079
#> 30: 1.346563 1.365079
#> 31: 1.346563 1.365079
#> 32: 1.346563 1.365079
#> 33: 1.346563 1.365079
#> 34: 1.346563 1.365079
#> 35: 1.346563 1.365079
#> 36: 1.346563 1.365079
#> elr_cc_ci_lo elr_cc_ci_hi
#> <num> <num>Apart from the absence of a prior argument, the call and
the output match Bornhuetter-Ferguson. It is the method to use when
there is no external basis for a prior and you let the portfolio speak
its own ELR.
fit_loss() / fit_premium() – the unified
dispatchers
Rather than calling a different function for each method,
fit_loss() lets you switch the method with a single
method argument.
method is one of "ed" (default),
"cl", "sa", "bf",
"cc". For "bf" / "cc" extra
arguments such as prior are forwarded through
.... fit_premium() is the companion function
that fits the premium side separately.
fe <- fit_premium(tri1)
summary(fe)
#> coverage cohort premium_ult premium_total_se premium_total_cv
#> <char> <Date> <num> <num> <num>
#> 1: surgery 2023-01-01 274192564 NA NA
#> 2: surgery 2023-02-01 665667720 203317.9 0.0003054339
#> 3: surgery 2023-03-01 702047332 262601.1 0.0003740529
#> 4: surgery 2023-04-01 1464399410 1367093.2 0.0009335767
#> 5: surgery 2023-05-01 483147255 703451.6 0.0014560085
#> 6: surgery 2023-06-01 591568799 1058731.8 0.0017897177
#> 7: surgery 2023-07-01 1958263736 3910208.1 0.0019968584
#> 8: surgery 2023-08-01 327535560 1828256.1 0.0055820892
#> 9: surgery 2023-09-01 1091733892 3952483.5 0.0036204828
#> 10: surgery 2023-10-01 864204933 3794976.2 0.0043913554
#> 11: surgery 2023-11-01 630311110 3272175.4 0.0051914680
#> 12: surgery 2023-12-01 1057060867 4484495.4 0.0042424185
#> 13: surgery 2024-01-01 2009045340 7688434.5 0.0038268640
#> 14: surgery 2024-02-01 832229795 4949366.6 0.0059470920
#> 15: surgery 2024-03-01 454345985 4045484.1 0.0089042245
#> 16: surgery 2024-04-01 3372494516 13992783.5 0.0041491213
#> 17: surgery 2024-05-01 1899849125 10075728.1 0.0053035580
#> 18: surgery 2024-06-01 750125230 6364391.3 0.0084844581
#> 19: surgery 2024-07-01 2891548085 14716651.1 0.0050896560
#> 20: surgery 2024-08-01 976935246 8364192.9 0.0085619202
#> 21: surgery 2024-09-01 703906575 7175630.7 0.0101943622
#> 22: surgery 2024-10-01 984833529 9313644.4 0.0094572623
#> 23: surgery 2024-11-01 324081360 5678519.9 0.0175216881
#> 24: surgery 2024-12-01 366444614 6236672.5 0.0170197403
#> 25: surgery 2025-01-01 833732378 10465225.2 0.0125525791
#> 26: surgery 2025-02-01 3286151352 23703310.8 0.0072131978
#> 27: surgery 2025-03-01 566316398 9534760.8 0.0168363975
#> 28: surgery 2025-04-01 476819833 10109619.3 0.0212023387
#> 29: surgery 2025-05-01 1027051048 16264024.8 0.0158367196
#> 30: surgery 2025-06-01 783037474 14618828.5 0.0186703135
#> 31: surgery 2025-07-01 859730812 17196880.8 0.0200032954
#> 32: surgery 2025-08-01 1037192185 21996644.0 0.0212094340
#> 33: surgery 2025-09-01 611257142 18778118.6 0.0307201006
#> 34: surgery 2025-10-01 1338462726 33336201.9 0.0249073599
#> 35: surgery 2025-11-01 593147593 24282233.8 0.0409388868
#> 36: surgery 2025-12-01 1022559927 47680639.5 0.0466199619
#> coverage cohort premium_ult premium_total_se premium_total_cv
#> <char> <Date> <num> <num> <num>
fit_ratio() – composing the loss ratio
fit_ratio() is the composition layer: it fits the loss
side and the premium side separately, then combines them to produce the
loss ratio.
lr <- fit_ratio(tri1, method = "sa")
summary(lr)
#> coverage cohort latest loss_ult reserve premium_ult
#> <char> <Date> <num> <num> <num> <num>
#> 1: surgery 2023-01-01 410248522 410248522 0 274192564
#> 2: surgery 2023-02-01 976330445 1001441303 25110858 665667720
#> 3: surgery 2023-03-01 978486045 1026151243 47665198 702047332
#> 4: surgery 2023-04-01 2029909919 2186771221 156861302 1464399410
#> 5: surgery 2023-05-01 624219436 697669301 73449865 483147255
#> 6: surgery 2023-06-01 802880717 931393934 128513217 591568799
#> 7: surgery 2023-07-01 2539141549 3050990158 511848609 1958263736
#> 8: surgery 2023-08-01 393678329 488218204 94539875 327535560
#> 9: surgery 2023-09-01 1364052542 1751869308 387816766 1091733892
#> 10: surgery 2023-10-01 979266043 1311793843 332527800 864204933
#> 11: surgery 2023-11-01 604685679 848103123 243417444 630311110
#> 12: surgery 2023-12-01 1026345366 1497869029 471523663 1057060867
#> 13: surgery 2024-01-01 1912177598 2901492851 989315253 2009045340
#> 14: surgery 2024-02-01 733902485 1160045952 426143467 832229795
#> 15: surgery 2024-03-01 415459873 686574148 271114275 454345985
#> 16: surgery 2024-04-01 3286053526 5687484014 2401430488 3372494516
#> 17: surgery 2024-05-01 1451731153 2645801838 1194070685 1899849125
#> 18: surgery 2024-06-01 629668308 1209024555 579356247 750125230
#> 19: surgery 2024-07-01 1250954693 2542927190 1291972497 2891548085
#> 20: surgery 2024-08-01 425346694 918120582 492773888 976935246
#> 21: surgery 2024-09-01 278156543 635470028 357313485 703906575
#> 22: surgery 2024-10-01 352070323 856446521 504376198 984833529
#> 23: surgery 2024-11-01 99050501 260916096 161865595 324081360
#> 24: surgery 2024-12-01 103194013 295637296 192443283 366444614
#> 25: surgery 2025-01-01 227089025 710560093 483471068 833732378
#> 26: surgery 2025-02-01 939163074 3276849152 2337686078 3286151352
#> 27: surgery 2025-03-01 112828845 434950057 322121212 566316398
#> 28: surgery 2025-04-01 82472453 356301148 273828695 476819833
#> 29: surgery 2025-05-01 141214851 697290587 556075736 1027051048
#> 30: surgery 2025-06-01 136406102 789468799 653062697 783037474
#> 31: surgery 2025-07-01 149144024 1040451732 891307708 859730812
#> 32: surgery 2025-08-01 116327076 1008356733 892029657 1037192185
#> 33: surgery 2025-09-01 67465470 783000257 715534787 611257142
#> 34: surgery 2025-10-01 121626173 2001214863 1879588690 1338462726
#> 35: surgery 2025-11-01 15716444 576954661 561238217 593147593
#> 36: surgery 2025-12-01 4825085 1246569307 1241744222 1022559927
#> coverage cohort latest loss_ult reserve premium_ult
#> <char> <Date> <num> <num> <num> <num>
#> ratio_latest ratio_ult maturity_from loss_proc_se loss_param_se
#> <num> <num> <num> <num> <num>
#> 1: 1.4962059 1.4962059 4 0 0
#> 2: 1.5107824 1.5044162 4 2974816 4362011
#> 3: 1.4771448 1.4616554 4 4270032 5160023
#> 4: 1.5139132 1.4932888 4 7041128 11598550
#> 5: 1.4543748 1.4440097 4 4511892 3807155
#> 6: 1.5796369 1.5744474 4 17444256 9252798
#> 7: 1.5597190 1.5580078 4 35085745 32956647
#> 8: 1.4945957 1.4905808 4 15581189 5527584
#> 9: 1.6079808 1.6046670 4 37754499 22337518
#> 10: 1.5129472 1.5179199 4 36292444 18145424
#> 11: 1.3298743 1.3455310 4 36448974 12573545
#> 12: 1.3981081 1.4170130 4 50088510 23067166
#> 13: 1.4274951 1.4442147 4 77086126 45322232
#> 14: 1.3793745 1.3939010 4 52024922 19053928
#> 15: 1.4969280 1.5111263 4 41835349 11430104
#> 16: 1.6712898 1.6864324 4 128329943 96356457
#> 17: 1.3770835 1.3926379 4 88940013 45748540
#> 18: 1.5918247 1.6117636 4 64461772 21226463
#> 19: 0.8658750 0.8794345 4 102590260 46504658
#> 20: 0.9236050 0.9397968 4 64598903 17104018
#> 21: 0.8920448 0.9027761 4 55690523 12099317
#> 22: 0.8596968 0.8696358 4 66391237 16462136
#> 23: 0.7871749 0.8050944 4 41431955 5297452
#> 24: 0.7813438 0.8067721 4 49894835 6370067
#> 25: 0.8188282 0.8522640 4 85025980 15999454
#> 26: 0.9377837 0.9971693 4 182877119 76356271
#> 27: 0.7193486 0.7680337 4 69632308 10311279
#> 28: 0.6947510 0.7472448 4 70309787 8715699
#> 29: 0.6203897 0.6789250 4 118636641 19479723
#> 30: 0.8981587 1.0082133 4 132736664 23023332
#> 31: 1.0440457 1.2102064 4 165733132 31664923
#> 32: 0.8100543 0.9721985 4 185534229 32540766
#> 33: 0.9985960 1.2809670 4 184367813 27287599
#> 34: 1.0894657 1.4951592 4 330089483 80102400
#> 35: 0.4765917 0.9727000 4 197962944 20848833
#> 36: 0.1689836 1.2190672 4 476510733 64518340
#> ratio_latest ratio_ult maturity_from loss_proc_se loss_param_se
#> <num> <num> <num> <num> <num>
#> loss_total_se loss_total_cv ratio_se ratio_cv ratio_ci_lo ratio_ci_hi
#> <num> <num> <num> <num> <num> <num>
#> 1: 0 0.000000000 0.000000000 0.000000000 1.4962059 1.4962059
#> 2: 5279836 0.005272237 0.007931639 0.005272237 1.4888705 1.5199619
#> 3: 6697687 0.006526998 0.009540221 0.006526998 1.4429569 1.4803538
#> 4: 13568488 0.006204804 0.009265565 0.006204804 1.4751286 1.5114490
#> 5: 5903524 0.008461780 0.012218892 0.008461780 1.4200611 1.4679582
#> 6: 19746299 0.021200803 0.033379548 0.021200803 1.5090246 1.6398701
#> 7: 48136785 0.015777430 0.024581360 0.015777430 1.5098292 1.6061864
#> 8: 16532623 0.033863185 0.050475812 0.033863185 1.3916500 1.5895115
#> 9: 43867607 0.025040456 0.040181593 0.025040456 1.5259125 1.6834214
#> 10: 40575829 0.030931560 0.046951629 0.030931560 1.4258964 1.6099434
#> 11: 38556734 0.045462318 0.061170958 0.045462318 1.2256381 1.4654238
#> 12: 55144837 0.036815526 0.052168081 0.036815526 1.3147655 1.5192606
#> 13: 89422455 0.030819464 0.044509924 0.030819464 1.3569769 1.5314526
#> 14: 55404374 0.047760500 0.066573409 0.047760500 1.2634195 1.5243825
#> 15: 43368695 0.063166805 0.095453018 0.063166805 1.3240418 1.6982107
#> 16: 160477852 0.028215965 0.047584318 0.028215965 1.5931688 1.7796959
#> 17: 100016273 0.037801876 0.052644324 0.037801876 1.2894569 1.4958188
#> 18: 67866655 0.056133397 0.090473767 0.056133397 1.4344383 1.7890889
#> 19: 112638558 0.044294842 0.038954413 0.044294842 0.8030853 0.9557838
#> 20: 66824889 0.072784436 0.068402577 0.072784436 0.8057302 1.0738634
#> 21: 56989717 0.089681204 0.080962047 0.089681204 0.7440934 1.0614588
#> 22: 68401742 0.079866916 0.069455131 0.079866916 0.7335063 1.0057654
#> 23: 41769245 0.160086887 0.128885060 0.160086887 0.5524843 1.0577045
#> 24: 50299824 0.170140320 0.137264466 0.170140320 0.5377387 1.0758055
#> 25: 86518205 0.121760574 0.103772154 0.121760574 0.6488743 1.0556537
#> 26: 198177499 0.060478066 0.060306869 0.060478066 0.8789700 1.1153686
#> 27: 70391625 0.161838408 0.124297345 0.161838408 0.5244153 1.0116520
#> 28: 70847933 0.198842842 0.148584283 0.198842842 0.4560250 1.0384647
#> 29: 120225256 0.172417723 0.117058695 0.172417723 0.4494941 0.9083558
#> 30: 134718580 0.170644590 0.172046146 0.170644590 0.6710091 1.3454176
#> 31: 168730965 0.162170872 0.196260228 0.162170872 0.8255434 1.5948694
#> 32: 188366269 0.186805188 0.181611732 0.186805188 0.6162461 1.3281510
#> 33: 186376242 0.238028328 0.304906445 0.238028328 0.6833614 1.8785727
#> 34: 339669635 0.169731717 0.253775939 0.169731717 0.9977675 1.9925509
#> 35: 199057783 0.345014602 0.335595702 0.345014602 0.3149445 1.6304555
#> 36: 480858705 0.385745664 0.470249902 0.385745664 0.2973944 2.1407401
#> loss_total_se loss_total_cv ratio_se ratio_cv ratio_ci_lo ratio_ci_hi
#> <num> <num> <num> <num> <num> <num>$full holds loss_proj /
premium_proj / ratio_proj together with the
loss-ratio standard error (ratio_se) and confidence
interval (ratio_ci_lo / ratio_ci_hi).
head(lr$full[, c("cohort", "dev", "loss_proj", "premium_proj",
"ratio_proj", "ratio_se")])
#> cohort dev loss_proj premium_proj ratio_proj ratio_se
#> <Date> <int> <num> <num> <num> <num>
#> 1: 2023-01-01 1 1886123 7527562 0.2505623 0
#> 2: 2023-01-01 2 14030514 15168591 0.9249715 0
#> 3: 2023-01-01 3 24427715 22794364 1.0716559 0
#> 4: 2023-01-01 4 34672477 31558907 1.0986590 0
#> 5: 2023-01-01 5 44990229 39336754 1.1437199 0
#> 6: 2023-01-01 6 55621697 47008228 1.1832332 0The loss-ratio standard error is governed by se_method:
"fixed" (default) treats premium as a known value, while
"delta" carries the uncertainty of premium and the
loss-premium correlation through the delta method.
plot(lr)
Calendar and Total – the other aggregation frameworks
The same long-format experience can be aggregated three ways
depending on the question. as_triangle() keeps both axes
(cohort x dev) for projection; two siblings collapse one or both
axes.
as_calendar() collapses cohorts onto the diagonal,
giving one row per calendar period – the diagonal sum of the triangle.
Use it for calendar-time trend and diagonal-effect analysis.
cal <- as_calendar(tri1)
head(cal)
#> shape: (6, 18)
#> ┌──────────┬────────────┬─────────┬───┬───────────────┬────────────────┐
#> │ coverage ┆ calendar ┆ cal_idx ┆ … ┆ premium_share ┆ incr_premium_… │
#> │ <chr> ┆ <date> ┆ <int> ┆ … ┆ <dbl> ┆ <dbl> │
#> ├──────────┼────────────┼─────────┼───┼───────────────┼────────────────┤
#> │ surgery ┆ 2023-01-01 ┆ 1 ┆ … ┆ 1 ┆ 1 │
#> │ surgery ┆ 2023-02-01 ┆ 2 ┆ … ┆ 1 ┆ 1 │
#> │ surgery ┆ 2023-03-01 ┆ 3 ┆ … ┆ 1 ┆ 1 │
#> │ surgery ┆ 2023-04-01 ┆ 4 ┆ … ┆ 1 ┆ 1 │
#> │ surgery ┆ 2023-05-01 ┆ 5 ┆ … ┆ 1 ┆ 1 │
#> │ surgery ┆ 2023-06-01 ┆ 6 ┆ … ┆ 1 ┆ 1 │
#> └──────────┴────────────┴─────────┴───┴───────────────┴────────────────┘
#> 13 more variables: n_cohorts <int>, loss <dbl>, incr_loss <dbl>, premium <dbl>,
#> incr_premium <dbl>, ratio <dbl>, incr_ratio <dbl>,
#> margin <dbl>, incr_margin <dbl>, profit <fct>,
#> incr_profit <fct>, loss_share <dbl>, incr_loss_share <dbl>
plot(cal) # x axis: calendar (Date)
The t column is a sequential index within group (1, 2,
3, …), a time-series convention. It is not a development
period.
as_total() collapses both axes to one value per group,
useful for portfolio-level comparison. The period_from /
period_to arguments bound a fixed window so groups stay
comparable.
tot <- as_total(
as_triangle(
experience[uy_m >= as.Date("2023-04-01") &
uy_m <= as.Date("2024-03-01")],
groups = "coverage", cohort = "uy_m", dev = "dev_m",
loss = "incr_loss", premium = "incr_premium"
)
)
head(tot)
#> shape: (4, 9)
#> ┌───────────┬───────────┬─────────────┬───┬────────────┬───────────────┐
#> │ coverage ┆ n_cohorts ┆ sales_start ┆ … ┆ loss_share ┆ premium_share │
#> │ <chr> ┆ <int> ┆ <date> ┆ … ┆ <dbl> ┆ <dbl> │
#> ├───────────┼───────────┼─────────────┼───┼────────────┼───────────────┤
#> │ ci ┆ 12 ┆ 2023-04-01 ┆ … ┆ 0.33461100 ┆ 0.427133 │
#> │ cancer ┆ 12 ┆ 2023-04-01 ┆ … ┆ 0.11375800 ┆ 0.162389 │
#> │ inpatient ┆ 12 ┆ 2023-04-01 ┆ … ┆ 0.00644687 ┆ 0.016502 │
#> │ surgery ┆ 12 ┆ 2023-04-01 ┆ … ┆ 0.54518400 ┆ 0.393976 │
#> └───────────┴───────────┴─────────────┴───┴────────────┴───────────────┘
#> 4 more variables: sales_end <date>, loss <dbl>, premium <dbl>, ratio <dbl>The Link object – factor-level diagnostics
Between a Triangle and a fit sits the Link object,
the per-link factor table built by as_link(). It is the
intermediate object that feeds both chain ladder and the exposure-driven
model.
# single-variable mode -> observed age-to-age factors
ata <- as_link(tri1, loss = "loss")
summary(ata, model = "ata")
#> Key: <coverage>
#> coverage ata_from ata_to ata_link mean median wt cv f f_se
#> <char> <num> <num> <fctr> <num> <num> <num> <num> <num> <num>
#> 1: surgery 1 2 1-2 6.595 6.089 6.163 0.427 6.163 0.382
#> 2: surgery 2 3 2-3 1.765 1.768 1.739 0.157 1.739 0.042
#> 3: surgery 3 4 3-4 1.435 1.400 1.418 0.105 1.418 0.027
#> 4: surgery 4 5 4-5 1.324 1.331 1.339 0.068 1.339 0.018
#> 5: surgery 5 6 5-6 1.267 1.246 1.243 0.070 1.243 0.016
#> 6: surgery 6 7 6-7 1.204 1.194 1.205 0.048 1.205 0.011
#> 7: surgery 7 8 7-8 1.163 1.158 1.172 0.045 1.172 0.011
#> 8: surgery 8 9 8-9 1.141 1.124 1.143 0.066 1.143 0.015
#> 9: surgery 9 10 9-10 1.127 1.131 1.121 0.030 1.121 0.006
#> 10: surgery 10 11 10-11 1.104 1.098 1.105 0.025 1.105 0.005
#> 11: surgery 11 12 11-12 1.110 1.108 1.115 0.029 1.115 0.007
#> 12: surgery 12 13 12-13 1.099 1.094 1.092 0.028 1.092 0.007
#> 13: surgery 13 14 13-14 1.085 1.078 1.088 0.026 1.088 0.007
#> 14: surgery 14 15 14-15 1.077 1.070 1.083 0.026 1.083 0.007
#> 15: surgery 15 16 15-16 1.064 1.063 1.065 0.018 1.065 0.003
#> 16: surgery 16 17 16-17 1.058 1.057 1.058 0.015 1.058 0.004
#> 17: surgery 17 18 17-18 1.057 1.055 1.062 0.015 1.062 0.004
#> 18: surgery 18 19 18-19 1.059 1.060 1.059 0.019 1.059 0.005
#> 19: surgery 19 20 19-20 1.055 1.057 1.054 0.015 1.054 0.003
#> 20: surgery 20 21 20-21 1.053 1.053 1.053 0.018 1.053 0.005
#> 21: surgery 21 22 21-22 1.046 1.046 1.047 0.012 1.047 0.003
#> 22: surgery 22 23 22-23 1.046 1.044 1.045 0.013 1.045 0.003
#> 23: surgery 23 24 23-24 1.046 1.040 1.042 0.018 1.042 0.004
#> 24: surgery 24 25 24-25 1.043 1.040 1.040 0.021 1.040 0.004
#> 25: surgery 25 26 25-26 1.046 1.042 1.041 0.018 1.041 0.005
#> 26: surgery 26 27 26-27 1.042 1.036 1.047 0.017 1.047 0.006
#> 27: surgery 27 28 27-28 1.040 1.034 1.043 0.014 1.043 0.005
#> 28: surgery 28 29 28-29 1.041 1.045 1.036 0.013 1.036 0.006
#> 29: surgery 29 30 29-30 1.035 1.033 1.032 0.008 1.032 0.003
#> 30: surgery 30 31 30-31 1.036 1.032 1.036 0.009 1.036 0.004
#> 31: surgery 31 32 31-32 1.041 1.038 1.038 0.016 1.038 0.008
#> 32: surgery 32 33 32-33 1.038 1.038 1.037 0.003 1.037 0.001
#> 33: surgery 33 34 33-34 1.027 1.026 1.027 0.003 1.027 0.002
#> 34: surgery 34 35 34-35 1.024 1.024 1.022 0.004 1.022 0.002
#> 35: surgery 35 36 35-36 1.026 1.026 1.026 NA 1.026 NA
#> coverage ata_from ata_to ata_link mean median wt cv f f_se
#> <char> <num> <num> <fctr> <num> <num> <num> <num> <num> <num>
#> rse sigma n_cohorts n_valid n_inf n_nan valid_ratio
#> <num> <num> <num> <num> <num> <num> <num>
#> 1: 0.062 6207.618 35 35 0 0 1
#> 2: 0.024 1689.250 34 34 0 0 1
#> 3: 0.019 1372.883 33 33 0 0 1
#> 4: 0.014 1105.053 32 32 0 0 1
#> 5: 0.013 1086.826 31 31 0 0 1
#> 6: 0.009 812.770 30 30 0 0 1
#> 7: 0.009 879.041 29 29 0 0 1
#> 8: 0.013 1364.524 28 28 0 0 1
#> 9: 0.006 619.261 27 27 0 0 1
#> 10: 0.004 482.198 26 26 0 0 1
#> 11: 0.006 720.023 25 25 0 0 1
#> 12: 0.007 760.455 24 24 0 0 1
#> 13: 0.007 821.580 23 23 0 0 1
#> 14: 0.006 754.516 22 22 0 0 1
#> 15: 0.003 402.657 21 21 0 0 1
#> 16: 0.004 453.146 20 20 0 0 1
#> 17: 0.004 492.253 19 19 0 0 1
#> 18: 0.005 599.191 18 18 0 0 1
#> 19: 0.003 388.598 17 17 0 0 1
#> 20: 0.005 614.425 16 16 0 0 1
#> 21: 0.003 322.569 15 15 0 0 1
#> 22: 0.003 345.135 14 14 0 0 1
#> 23: 0.004 477.542 13 13 0 0 1
#> 24: 0.004 386.326 12 12 0 0 1
#> 25: 0.004 439.006 11 11 0 0 1
#> 26: 0.005 541.166 10 10 0 0 1
#> 27: 0.005 498.003 9 9 0 0 1
#> 28: 0.006 522.482 8 8 0 0 1
#> 29: 0.003 253.107 7 7 0 0 1
#> 30: 0.004 267.272 6 6 0 0 1
#> 31: 0.008 540.332 5 5 0 0 1
#> 32: 0.001 78.583 4 4 0 0 1
#> 33: 0.002 81.016 3 3 0 0 1
#> 34: 0.002 88.069 2 2 0 0 1
#> 35: NA NA 1 1 0 0 1
#> rse sigma n_cohorts n_valid n_inf n_nan valid_ratio
#> <num> <num> <num> <num> <num> <num> <num>
# dual-variable mode -> exposure-driven intensities g_k
ed_link <- as_link(tri1, loss = "loss", exposure = "premium")
summary(ed_link, model = "ed")
#> Key: <coverage>
#> coverage ata_from ata_to ata_link mean median wt cv g
#> <char> <num> <num> <fctr> <num> <num> <num> <num> <num>
#> 1: surgery 1 2 1-2 1.34661 1.21766 1.31614 0.47327 1.31614
#> 2: surgery 2 3 2-3 0.58109 0.56432 0.58674 0.37381 0.58674
#> 3: surgery 3 4 3-4 0.39105 0.36751 0.38178 0.43535 0.38178
#> 4: surgery 4 5 4-5 0.31110 0.32321 0.33127 0.35969 0.33127
#> 5: surgery 5 6 5-6 0.27543 0.25088 0.25518 0.43531 0.25518
#> 6: surgery 6 7 6-7 0.21364 0.20479 0.22393 0.31371 0.22393
#> 7: surgery 7 8 7-8 0.18072 0.18227 0.19476 0.36392 0.19476
#> 8: surgery 8 9 8-9 0.16798 0.15484 0.16849 0.67814 0.16849
#> 9: surgery 9 10 9-10 0.14955 0.13195 0.14572 0.33906 0.14572
#> 10: surgery 10 11 10-11 0.12550 0.12095 0.12851 0.31241 0.12851
#> 11: surgery 11 12 11-12 0.13833 0.12898 0.14581 0.39551 0.14581
#> 12: surgery 12 13 12-13 0.12519 0.11356 0.12075 0.34186 0.12075
#> 13: surgery 13 14 13-14 0.11144 0.10927 0.11631 0.35239 0.11631
#> 14: surgery 14 15 14-15 0.10561 0.09421 0.11169 0.43662 0.11169
#> 15: surgery 15 16 15-16 0.08954 0.08726 0.08964 0.34359 0.08964
#> 16: surgery 16 17 16-17 0.08079 0.07993 0.08162 0.24700 0.08162
#> 17: surgery 17 18 17-18 0.08109 0.07612 0.08725 0.28780 0.08725
#> 18: surgery 18 19 18-19 0.08636 0.08620 0.08772 0.34300 0.08772
#> 19: surgery 19 20 19-20 0.07944 0.07838 0.08008 0.25109 0.08008
#> 20: surgery 20 21 20-21 0.07789 0.07935 0.08007 0.32197 0.08007
#> 21: surgery 21 22 21-22 0.06746 0.06606 0.06982 0.26290 0.06982
#> 22: surgery 22 23 22-23 0.06748 0.06394 0.06703 0.32299 0.06703
#> 23: surgery 23 24 23-24 0.06644 0.05971 0.06165 0.39463 0.06165
#> 24: surgery 24 25 24-25 0.06303 0.05711 0.05902 0.45911 0.05902
#> 25: surgery 25 26 25-26 0.06696 0.06136 0.06056 0.39347 0.06056
#> 26: surgery 26 27 26-27 0.06265 0.05387 0.07093 0.44081 0.07093
#> 27: surgery 27 28 27-28 0.06010 0.05136 0.06550 0.36862 0.06550
#> 28: surgery 28 29 28-29 0.06012 0.06544 0.05404 0.31348 0.05404
#> 29: surgery 29 30 29-30 0.05275 0.04745 0.04877 0.23587 0.04877
#> 30: surgery 30 31 30-31 0.05437 0.04834 0.05359 0.25583 0.05359
#> 31: surgery 31 32 31-32 0.06003 0.05618 0.05643 0.41162 0.05643
#> 32: surgery 32 33 32-33 0.05749 0.05671 0.05622 0.07265 0.05622
#> 33: surgery 33 34 33-34 0.04049 0.03873 0.04100 0.08481 0.04100
#> 34: surgery 34 35 34-35 0.03562 0.03562 0.03403 0.15183 0.03403
#> 35: surgery 35 36 35-36 0.03864 0.03864 0.03864 NA 0.03864
#> coverage ata_from ata_to ata_link mean median wt cv g
#> <char> <num> <num> <fctr> <num> <num> <num> <num> <num>
#> g_se rse sigma n_cohorts n_valid n_inf n_nan valid_ratio
#> <num> <num> <num> <num> <num> <num> <num> <num>
#> 1: 0.09107 0.06919 2930.74379 35 35 0 0 1
#> 2: 0.03508 0.05979 1580.26206 34 34 0 0 1
#> 3: 0.02931 0.07677 1587.18687 33 33 0 0 1
#> 4: 0.02135 0.06444 1319.11056 32 32 0 0 1
#> 5: 0.02087 0.08178 1421.47805 31 31 0 0 1
#> 6: 0.01273 0.05686 937.78642 30 30 0 0 1
#> 7: 0.01141 0.05860 897.25756 29 29 0 0 1
#> 8: 0.02169 0.12870 1792.82291 28 28 0 0 1
#> 9: 0.00943 0.06471 819.85457 27 27 0 0 1
#> 10: 0.00676 0.05263 614.41506 26 26 0 0 1
#> 11: 0.01185 0.08130 1065.55644 25 25 0 0 1
#> 12: 0.00987 0.08170 911.69544 24 24 0 0 1
#> 13: 0.01111 0.09556 1061.51299 23 23 0 0 1
#> 14: 0.01140 0.10209 1123.12989 22 22 0 0 1
#> 15: 0.00630 0.07031 629.63157 21 21 0 0 1
#> 16: 0.00475 0.05825 483.04483 20 20 0 0 1
#> 17: 0.00628 0.07198 644.16296 19 19 0 0 1
#> 18: 0.00745 0.08497 734.39263 18 18 0 0 1
#> 19: 0.00438 0.05473 434.93473 17 17 0 0 1
#> 20: 0.00692 0.08645 667.93909 16 16 0 0 1
#> 21: 0.00444 0.06361 392.59516 15 15 0 0 1
#> 22: 0.00501 0.07472 445.50689 14 14 0 0 1
#> 23: 0.00644 0.10443 566.66986 13 13 0 0 1
#> 24: 0.00532 0.09006 436.45244 12 12 0 0 1
#> 25: 0.00638 0.10534 505.82971 11 11 0 0 1
#> 26: 0.00878 0.12380 684.49354 10 10 0 0 1
#> 27: 0.00834 0.12727 627.18471 9 9 0 0 1
#> 28: 0.00853 0.15779 604.48158 8 8 0 0 1
#> 29: 0.00428 0.08784 300.99607 7 7 0 0 1
#> 30: 0.00553 0.10315 325.88934 6 6 0 0 1
#> 31: 0.01155 0.20459 641.18962 5 5 0 0 1
#> 32: 0.00153 0.02721 80.36415 4 4 0 0 1
#> 33: 0.00211 0.05148 81.83368 3 3 0 0 1
#> 34: 0.00348 0.10217 103.52601 2 2 0 0 1
#> 35: NA NA NA 1 1 0 0 1
#> g_se rse sigma n_cohorts n_valid n_inf n_nan valid_ratio
#> <num> <num> <num> <num> <num> <num> <num> <num>In single-variable mode (loss only) the Link carries the
observed age-to-age factors. Supplying exposure adds the
exposure-driven intensity
intensity = loss_delta / premium_from. The
summary() method computes the per-link statistics – mean /
median / weighted factor, coefficient of variation, WLS standard error –
that drive maturity detection. The factor-level helpers
fit_ata() and fit_intensity() wrap this same
machinery and return per-link estimates only (no $full
projection).
Diagnostics – maturity, convergence, regime
There are diagnostic functions for inspecting the triangle’s structure before and after fitting.
Maturity point – the development period where the age-to-age factor settles. It is also the stage-switch point of the stage-adaptive method.
detect_maturity(tri1)
#> Key: <coverage>
#> coverage ata_from change ata_link mean median wt cv
#> <char> <num> <num> <char> <num> <num> <num> <num>
#> 1: surgery 3 4 3-4 1.434507 1.400098 1.417706 0.1053282
#> f f_se rse sigma n_cohorts n_valid n_inf n_nan
#> <num> <num> <num> <num> <num> <num> <num> <num>
#> 1: 1.417706 0.02651852 0.01870522 1372.883 33 33 0 0
#> valid_ratio
#> <num>
#> 1: 1Convergence point – the development period beyond which the projected loss ratio no longer moves meaningfully. As the denominator of the cumulative loss ratio grows it dampens the signal – an inertia effect – which a dual criterion is used to filter through.
detect_convergence(tri1)
#> <Convergence>
#> method : tail
#> conv_k : NA
#> mat_k : 4
#> dev_max : 36
#> candidates : 31
#> passes :
#> window : 0/31 (drift_window < 0.01 & dispersion < 0.15)
#> tail : 0/31 (drift_tail < 0.01 & dispersion < 0.15) <- method
#> slope : 1/31 (|slope| < 0.001 & dispersion < 0.15)
#> all : 0/31 (window AND tail AND slope)Regime – a structural change between underwriting cohorts. It detects whether a premium, policy-wording, or underwriting-guideline change altered the loss behaviour of cohorts after a certain point.
reg <- detect_regime(tri)
reg$changes
#> coverage change regime_id pre_value post_value magnitude
#> <char> <Date> <int> <num> <num> <num>
#> 1: surgery 2024-07-01 2 0.9065895 0.5479919 0.3585976The surgery product in experience has a synthetic regime
change planted during 2024, so the result above picks up that change
point.
backtest() – validation
backtest() hides the latest few calendar diagonals,
refits the model, and compares the withheld actuals against the
projection to measure the model’s accuracy.
bt <- backtest(tri1, holdout = 6L, target = "ratio", loss_method = "sa")
summary(bt)
#> Backtest summary
#> dispatcher: fit_ratio
#> target : ratio
#> holdout : 6 diagonals (159 cells)
#>
#> By dev:
#> coverage dev n aeg_mean aeg_med ae_err_mean
#> <char> <int> <int> <num> <num> <num>
#> 1: surgery 2 1 -0.2879720892 -0.2879720892 -0.3667493406
#> 2: surgery 3 2 -0.1058236209 -0.1058236209 -0.0901195589
#> 3: surgery 4 3 -0.0438970022 0.0217666029 -0.0230071083
#> 4: surgery 5 4 -0.0110558266 0.0054351372 0.0118645748
#> 5: surgery 6 5 -0.0160114000 0.0370902061 0.0134987613
#> 6: surgery 7 6 0.0066390570 0.0520519271 0.0354091701
#> 7: surgery 8 6 0.0387556832 0.0468493428 0.0591624141
#> 8: surgery 9 6 0.0165983758 0.0181339640 0.0244533252
#> 9: surgery 10 6 0.0177699119 0.0134168699 0.0253607766
#> 10: surgery 11 6 0.0191431289 0.0114886577 0.0231290386
#> 11: surgery 12 6 0.0007211923 0.0015017408 0.0006387361
#> 12: surgery 13 6 0.0157220903 0.0076137593 0.0186533032
#> 13: surgery 14 6 0.0146558512 0.0269373691 0.0203566313
#> 14: surgery 15 6 -0.0164147403 -0.0078793254 -0.0085724729
#> 15: surgery 16 6 -0.0053773998 -0.0036509669 -0.0020439585
#> 16: surgery 17 6 0.0030866922 -0.0028402355 0.0055714790
#> 17: surgery 18 6 -0.0125129664 -0.0247929775 -0.0069398934
#> 18: surgery 19 6 -0.0113103120 -0.0086054969 -0.0082932779
#> 19: surgery 20 6 -0.0211209295 -0.0300370470 -0.0146794960
#> 20: surgery 21 6 -0.0123320969 -0.0288302132 -0.0081315596
#> 21: surgery 22 6 -0.0265367863 -0.0357010146 -0.0174246731
#> 22: surgery 23 6 -0.0241615696 -0.0113727688 -0.0160124793
#> 23: surgery 24 6 0.0023608518 0.0086349370 0.0019991795
#> 24: surgery 25 6 -0.0122696331 -0.0177060339 -0.0080061801
#> 25: surgery 26 6 0.0028673644 -0.0154389229 0.0029017289
#> 26: surgery 27 6 -0.0022551943 -0.0219579321 -0.0005984627
#> 27: surgery 28 6 0.0021536077 0.0005528274 0.0021335463
#> 28: surgery 29 6 0.0179714842 0.0123131943 0.0130930298
#> 29: surgery 30 6 -0.0039272898 0.0020727095 -0.0024107193
#> coverage dev n aeg_mean aeg_med ae_err_mean
#> <char> <int> <int> <num> <num> <num>
#> ae_err_med ae_err_wt incr_aeg_mean incr_aeg_med incr_ae_err_mean
#> <num> <num> <num> <num> <num>
#> 1: -0.3667493406 -0.3667493406 -0.57495418 -0.574954175 -0.42911219
#> 2: -0.0901195589 -0.1544635152 -0.03295105 -0.032951048 0.03104206
#> 3: 0.0437848471 -0.0656622116 0.03896663 -0.060404427 0.07170889
#> 4: 0.0123517418 -0.0162647786 0.07049188 0.081146126 0.09271533
#> 5: 0.0621128725 -0.0220352052 -0.04049602 0.091444980 0.04486252
#> 6: 0.0757446843 0.0088632803 0.12761981 0.080299453 0.16250805
#> 7: 0.0725907702 0.0550856653 0.02069969 0.007197477 0.01564729
#> 8: 0.0277518849 0.0223891429 -0.10613396 -0.136121764 -0.13147267
#> 9: 0.0171529396 0.0229537555 0.11236174 0.105535088 0.15605437
#> 10: 0.0154512077 0.0237389543 0.15969892 0.189675674 0.19686096
#> 11: 0.0018922252 0.0008808334 -0.08257465 -0.094057006 -0.08660181
#> 12: 0.0090087054 0.0190934981 0.17134975 0.064672398 0.19168084
#> 13: 0.0321857613 0.0152643056 -0.02644494 -0.114754500 0.01007152
#> 14: -0.0079107504 -0.0151493835 -0.41106393 -0.321970213 -0.28852360
#> 15: -0.0044851592 -0.0044371719 0.19818694 0.117799240 0.15063258
#> 16: -0.0018539369 0.0023518033 0.15672998 0.256737634 0.16971640
#> 17: -0.0169311833 -0.0088467233 -0.13589998 -0.185237736 -0.06313735
#> 18: -0.0054623225 -0.0075105462 0.06448340 0.048368896 0.03305654
#> 19: -0.0209835277 -0.0141893838 -0.17389925 -0.113722964 -0.11085823
#> 20: -0.0195936468 -0.0083339178 0.04888552 -0.116631342 0.04109121
#> 21: -0.0241489266 -0.0181905096 -0.22822576 -0.207832035 -0.14657964
#> 22: -0.0079804501 -0.0164674504 -0.14845744 -0.096634453 -0.09654333
#> 23: 0.0070443849 0.0016326821 0.16627897 -0.261922846 0.12001108
#> 24: -0.0128789134 -0.0083069614 -0.21608907 -0.189756124 -0.13659900
#> 25: -0.0098650416 0.0019209162 0.07312011 -0.164382561 0.05824859
#> 26: -0.0142767203 -0.0014781843 -0.32083035 -0.625762580 -0.17477888
#> 27: 0.0004018279 0.0014147005 0.06914757 -0.017229197 0.04186226
#> 28: 0.0081992616 0.0120992517 0.44252486 0.663837977 0.34283700
#> 29: 0.0012135586 -0.0026098433 -0.14700411 -0.270271875 -0.09019624
#> ae_err_med ae_err_wt incr_aeg_mean incr_aeg_med incr_ae_err_mean
#> <num> <num> <num> <num> <num>
#> incr_ae_err_med incr_ae_err_wt
#> <num> <num>
#> 1: -0.429112189 -0.42911219
#> 2: 0.031042058 -0.03788330
#> 3: -0.051312889 0.04819216
#> 4: 0.101566115 0.08262484
#> 5: 0.130130156 -0.04711615
#> 6: 0.136743653 0.14894131
#> 7: 0.008088929 0.02505782
#> 8: -0.163940480 -0.12387084
#> 9: 0.125264952 0.13525827
#> 10: 0.236016698 0.19825482
#> 11: -0.093881374 -0.08139958
#> 12: 0.070449982 0.19355031
#> 13: -0.124397482 -0.02436243
#> 14: -0.299928631 -0.30564120
#> 15: 0.148772947 0.17845143
#> 16: 0.285614433 0.13524568
#> 17: -0.124958477 -0.09463269
#> 18: 0.033222595 0.04168906
#> 19: -0.074261725 -0.11230739
#> 20: -0.069418132 0.03288272
#> 21: -0.133308413 -0.14878192
#> 22: -0.064872712 -0.09810761
#> 23: -0.190149810 0.11735901
#> 24: -0.131504726 -0.14062139
#> 25: -0.103229976 0.04391763
#> 26: -0.317754317 -0.16402220
#> 27: -0.009548040 0.04577902
#> 28: 0.509453512 0.33144073
#> 29: -0.165797630 -0.08977373
#> incr_ae_err_med incr_ae_err_wt
#> <num> <num>
#>
#> By calendar diagonal:
#> coverage cal_idx n aeg_mean aeg_med ae_err_mean ae_err_med
#> <char> <int> <int> <num> <num> <num> <num>
#> 1: surgery 31 29 -0.0125686252 -0.0056732350 -0.011309410 -0.003699313
#> 2: surgery 32 28 -0.0104717812 -0.0114871218 -0.002794292 -0.009588959
#> 3: surgery 33 27 0.0004718616 0.0050471735 0.007666312 0.006154835
#> 4: surgery 34 26 0.0012851467 -0.0002953897 0.008094503 0.000421251
#> 5: surgery 35 25 -0.0006986581 0.0145835308 0.007408947 0.009455704
#> 6: surgery 36 24 -0.0027175011 0.0105940082 0.005874139 0.009450279
#> ae_err_wt incr_aeg_mean incr_aeg_med incr_ae_err_mean incr_ae_err_med
#> <num> <num> <num> <num> <num>
#> 1: -0.0107004533 -0.08350070 -0.07460811 -0.036347452 -0.06750071
#> 2: -0.0089044278 -0.07573837 -0.07440057 -0.003857981 -0.07262916
#> 3: 0.0004012161 0.18105966 0.09849605 0.147072061 0.12954698
#> 4: 0.0010973317 0.01407124 -0.02312661 0.017058138 -0.02473897
#> 5: -0.0005997009 -0.03104560 -0.09210258 -0.008476082 -0.07819464
#> 6: -0.0023535415 -0.06224227 -0.09299902 -0.016968983 -0.09358995
#> incr_ae_err_wt
#> <num>
#> 1: -0.06558617
#> 2: -0.06014060
#> 3: 0.14477037
#> 4: 0.01130928
#> 5: -0.02508022
#> 6: -0.05088339target is one of "ratio" /
"loss" / "premium", calling
fit_ratio / fit_loss /
fit_premium internally. The resulting A/E error tables show
which development periods and which diagonals the model missed.
plot(bt)
Visualisation – plot() /
plot_triangle()
Every major object supports two families of plots.
-
plot(x)– trajectory / diagnostic charts (per-cohort development curves, regime PCA, and so on). -
plot_triangle(x)– triangular heatmaps (cell values or cell status).
plot_triangle(sa, label_style = "cv")
The label_style argument of plot_triangle()
switches the cell labels between value ("value"),
coefficient of variation ("cv"), standard error
("se"), and confidence interval ("ci"). For
the detailed arguments of plot() – type,
region, and so on – see each class’s help page
(?plot.CLFit and friends).
The CL / ED / SA / BF / CC / premium fit results all support
plot() and plot_triangle() the same way, so
the visualisation interface is identical regardless of method.
See also
This tutorial follows the core workflow in one pass. For the methodological background and detailed options of each topic, see:
-
?as_triangle,?fit_cl,?fit_sa,?fit_ratioand other per-function help pages. -
vignette("projection")– projection methods in depth. -
vignette("diagnostics")– maturity, convergence, and regime detection. -
vignette("backtest")– the validation procedure. -
vignette("bootstrap-se-decomposition")– bootstrap standard errors and variance decomposition.