영어 원본 보기: Getting started with lossratio
이 문서는 lossratio 의 전체 파이프라인을 내장 합성
experience 데이터 위에서 따라간다. long-format raw 데이터에서 시작하여
적합된 손해율 추정까지 이어진다.
입력 형태
lossratio 는 long-format experience 데이터를 입력으로
사용한다 — 한 행은 (코호트 × 경과 기간 × 인구통계) 셀 하나에 대응한다.
내장 데이터셋 experience 는 33,480 행 테이블로, 여러 단위의
calendar / underwriting 기간 컬럼, 인구통계 차원 (cv_nm,
age_band, gender), 금액 컬럼
(loss, rp) 을 포함한다.
library(lossratio)
data(experience)
str(experience)
#> Classes 'data.table' and 'data.frame': 33480 obs. of 17 variables:
#> $ cy : Date, format: "2023-01-01" "2023-01-01" ...
#> $ cyh : Date, format: "2023-01-01" "2023-01-01" ...
#> $ cyq : Date, format: "2023-04-01" "2023-04-01" ...
#> $ cym : Date, format: "2023-04-01" "2023-04-01" ...
#> $ uy : Date, format: "2023-01-01" "2023-01-01" ...
#> $ uyh : Date, format: "2023-01-01" "2023-01-01" ...
#> $ uyq : Date, format: "2023-04-01" "2023-04-01" ...
#> $ uym : Date, format: "2023-04-01" "2023-04-01" ...
#> $ elap_y : int 1 1 1 1 1 1 1 1 1 1 ...
#> $ elap_h : int 1 1 1 1 1 1 1 1 1 1 ...
#> $ elap_q : int 1 1 1 1 1 1 1 1 1 1 ...
#> $ elap_m : int 1 1 1 1 1 1 1 1 1 1 ...
#> $ cv_nm : chr "SUR" "SUR" "SUR" "SUR" ...
#> $ age_band: Ord.factor w/ 9 levels "30-34"<"35-39"<..: 1 1 2 2 3 3 4 4 5 5 ...
#> $ gender : Factor w/ 2 levels "M","F": 1 2 1 2 1 2 1 2 1 2 ...
#> $ loss : num 0 0 0 0 0 0 0 0 0 0 ...
#> $ rp : num 3555865 258448 255420 464313 92744 ...
#> - attr(*, ".internal.selfref")=<pointer: (nil)>1단계 — 검증 및 코어션
exp <- as_experience(experience)
class(exp)
#> [1] "Experience" "data.table" "data.frame"as_experience() 는 필수 컬럼 (cym,
uym, loss, rp) 의 존재를
확인하고, 날짜 컬럼을 코어션하며, 클래스를 부여한다. 변형 없이 검증만
필요하면 check_experience(df) 를 사용한다.
2단계 — 코호트 × 경과 기간 구조 구축
tri <- build_triangle(exp[cv_nm == "SUR"], group_var = cv_nm)
class(tri)
#> [1] "Triangle" "data.table" "data.frame"
names(tri)
#> [1] "cv_nm" "n_obs" "cohort" "dev" "loss"
#> [6] "rp" "closs" "crp" "margin" "cmargin"
#> [11] "profit" "cprofit" "lr" "clr" "loss_prop"
#> [16] "rp_prop" "closs_prop" "crp_prop"build_triangle() 의 동작:
- 인구통계 차원을 집계하여 제거한다 (여기서는
age_band,gender), - 누적 컬럼 (
closs,crp) 을 추가한다, - 파생 지표 (
margin,lr,clr, 비율) 를 추가한다, - 코호트 / 경과 기간 컬럼을 표준명
cohort와dev로 rename 한다, - 원본 컬럼명은 attribute (
cohort_var,dev_var) 로 보존하여 이후 plot 라벨에서 활용 가능하게 한다.
3단계 — 진단
plot(tri) # 코호트별 clr 궤적
plot_triangle(tri) # clr 셀의 heatmap
summary(tri) # 경과 기간별 그룹 통계량
#> Key: <cv_nm, dev>
#> cv_nm dev n_obs lr_mean lr_median lr_wt clr_mean clr_median
#> <char> <int> <int> <num> <num> <num> <num> <num>
#> 1: SUR 1 30 0.0738546 0.0000000 0.07343113 0.0738546 0.0000000
#> 2: SUR 2 29 0.5365888 0.0992849 0.54126362 0.3512535 0.1120447
#> 3: SUR 3 28 0.6201189 0.2472070 0.56590118 0.4521326 0.2618096
#> 4: SUR 4 27 0.8852657 0.6387164 0.92060611 0.6327242 0.4798531
#> 5: SUR 5 26 0.5767556 0.4828899 0.59880663 0.6369307 0.5641166
#> 6: SUR 6 25 0.9314593 0.5431397 0.95085711 0.7264308 0.6191132
#> 7: SUR 7 24 0.8240033 0.6252286 0.77687370 0.7555932 0.7992795
#> 8: SUR 8 23 1.1675190 0.7248212 1.27544718 0.8676101 0.7931337
#> 9: SUR 9 22 0.7525589 0.6155797 0.80158895 0.8755390 0.7890790
#> 10: SUR 10 21 0.8335086 0.6979443 0.76977519 0.8760001 0.7896553
#> 11: SUR 11 20 0.9673902 0.8800705 1.00022912 0.8967165 0.8355443
#> 12: SUR 12 19 0.8517931 0.6947156 0.85401463 0.9051208 0.8833728
#> 13: SUR 13 18 1.0020059 0.8967964 0.98253067 0.9362016 0.9420986
#> 14: SUR 14 17 1.0962361 1.0738800 1.16483245 0.9869708 1.0624927
#> 15: SUR 15 16 0.7760479 0.8230115 0.80108577 0.9870392 1.0459131
#> 16: SUR 16 15 0.8254441 0.6962883 0.85204193 0.9992647 1.0388452
#> 17: SUR 17 14 0.9058332 0.8098679 0.90979966 1.0121916 1.0649114
#> 18: SUR 18 13 1.0184650 1.0848554 1.00362430 1.0518881 1.0717561
#> 19: SUR 19 12 1.1760267 1.0964987 1.16189899 1.0931503 1.1135768
#> 20: SUR 20 11 1.0221131 1.0224721 1.00298630 1.1006314 1.1221288
#> 21: SUR 21 10 1.2370057 1.1559477 1.24931320 1.1032718 1.1256455
#> 22: SUR 22 9 1.1949424 1.1807304 1.17762170 1.1065793 1.1255582
#> 23: SUR 23 8 1.2851680 1.3577496 1.31179285 1.1060777 1.1285479
#> 24: SUR 24 7 1.0598906 0.8375035 1.13727404 1.1000157 1.0774681
#> 25: SUR 25 6 0.9385597 0.9798018 0.95054947 1.0833124 1.0638356
#> 26: SUR 26 5 0.8196121 0.9665387 0.85145986 1.0923577 1.0737966
#> 27: SUR 27 4 1.0466054 1.0672777 1.03231128 1.0684910 1.0866012
#> 28: SUR 28 3 0.9876176 0.5356686 1.20396265 1.0678995 1.0663302
#> 29: SUR 29 2 0.9678421 0.9678421 0.96314465 1.0004101 1.0004101
#> 30: SUR 30 1 0.8877097 0.8877097 0.88770973 0.9318395 0.9318395
#> cv_nm dev n_obs lr_mean lr_median lr_wt clr_mean clr_median
#> <char> <int> <int> <num> <num> <num> <num> <num>
#> clr_wt
#> <num>
#> 1: 0.07343113
#> 2: 0.35150128
#> 3: 0.44744109
#> 4: 0.63467048
#> 5: 0.63999290
#> 6: 0.72781355
#> 7: 0.75210593
#> 8: 0.86554028
#> 9: 0.87613232
#> 10: 0.87381694
#> 11: 0.89806835
#> 12: 0.90531724
#> 13: 0.93753009
#> 14: 0.98899894
#> 15: 0.99133864
#> 16: 1.00482935
#> 17: 1.01782259
#> 18: 1.05697013
#> 19: 1.09700313
#> 20: 1.10409515
#> 21: 1.10555289
#> 22: 1.10949324
#> 23: 1.10906728
#> 24: 1.10067296
#> 25: 1.08291578
#> 26: 1.09382873
#> 27: 1.07050979
#> 28: 1.07487952
#> 29: 0.99818417
#> 30: 0.93183949
#> clr_wt
#> <num>4단계 — 경과 기간 모형화
코호트 발달을 보는 두 가지 상호 보완적 관점.
# ATA 인자(age-to-age factor)
ata <- build_ata(tri, value_var = "closs")
fit_ata(ata)
#> <ATAFit>
#> alpha : 1
#> sigma_method: min_last2
#> recent : all
#> regime_break: none
#> use_maturity: FALSE
#> groups : cv_nm
#> n_groups : 1
#> ata links : 29
# 노출 기반(exposure-driven) 강도
ed <- build_ed(tri, loss_var = "closs", exposure_var = "crp")
fit_ed(ed)
#> <EDFit>
#> method : basic
#> loss_var : closs
#> exposure_var: crp
#> alpha : 1
#> sigma_method: min_last2
#> recent : all
#> regime_break: none
#> groups : cv_nm
#> n_groups : 1
#> links : 29fit_ata() 는 경과 기간 링크별로 선택된 ATA 인자를
반환한다. fit_ed() 는 강도 인자
를 반환한다. 두 출력 모두 아래 추정 방법의 입력으로 사용된다.
5단계 — 추정
fit_cl() 은 chain ladder 추정을 수행한다.
summary(cl)
#> cv_nm cohort latest ultimate reserve proc_se param_se
#> <char> <Date> <num> <num> <num> <num> <num>
#> 1: SUR 2023-04-01 2442597048 2442597048 0 0.0 0.0
#> 2: SUR 2023-05-01 2423543638 2600462324 176918686 270023.8 278555.7
#> 3: SUR 2023-06-01 3211045460 3634951626 423906166 461673.6 481436.4
#> 4: SUR 2023-07-01 2552396709 3106052713 553656004 217960839.6 130390124.6
#> 5: SUR 2023-08-01 2472997706 3159902325 686904619 235800277.9 139803599.9
#> 6: SUR 2023-09-01 2014222417 2712676349 698453932 230925350.1 124174149.3
#> 7: SUR 2023-10-01 2422172254 3464336723 1042164469 276909538.1 163800531.1
#> 8: SUR 2023-11-01 2157147612 3350616805 1193469193 347646646.1 180286627.2
#> 9: SUR 2023-12-01 2062030017 3510350121 1448320104 379204803.4 195291838.6
#> 10: SUR 2024-01-01 1803809914 3316423447 1512613533 371903391.7 185291186.8
#> 11: SUR 2024-02-01 1627213157 3293904272 1666691115 406210629.2 191768888.6
#> 12: SUR 2024-03-01 1006624213 2212909862 1206285649 348109439.7 131371151.5
#> 13: SUR 2024-04-01 707083237 1712964993 1005881756 316686848.8 103164315.5
#> 14: SUR 2024-05-01 398857325 1069653556 670796231 262671178.8 65778222.8
#> 15: SUR 2024-06-01 558855276 1654603718 1095748442 342800640.3 103939643.9
#> 16: SUR 2024-07-01 423131371 1378042306 954910935 336548946.6 89486750.7
#> 17: SUR 2024-08-01 457705980 1642689597 1184983617 387322897.0 109347246.8
#> 18: SUR 2024-09-01 278007651 1166380310 888372659 360265104.1 81491440.0
#> 19: SUR 2024-10-01 214811381 1027414214 812602833 358796880.9 74015042.1
#> 20: SUR 2024-11-01 251273971 1400108561 1148834590 451728990.6 105050619.0
#> 21: SUR 2024-12-01 322678179 2168358632 1845680453 619598522.3 171876903.1
#> 22: SUR 2025-01-01 179253475 1403314539 1224061064 523388251.8 114399770.9
#> 23: SUR 2025-02-01 100816665 954214626 853397961 497168458.4 84734261.7
#> 24: SUR 2025-03-01 111279087 1488227953 1376948866 843027195.9 163376024.6
#> 25: SUR 2025-04-01 55914454 958667529 902753075 751897091.4 113958278.9
#> 26: SUR 2025-05-01 41578391 1041506115 999927724 978637599.4 147793339.1
#> 27: SUR 2025-06-01 14997314 484991215 469993901 813441277.3 81273429.5
#> 28: SUR 2025-07-01 6232031 436725855 430493824 5630776358.8 495928426.0
#> 29: SUR 2025-08-01 0 0 0 0.0 0.0
#> 30: SUR 2025-09-01 0 0 0 0.0 0.0
#> cv_nm cohort latest ultimate reserve proc_se param_se
#> <char> <Date> <num> <num> <num> <num> <num>
#> se cv
#> <num> <num>
#> 1: 0.0 0.000000e+00
#> 2: 387951.2 1.491855e-04
#> 3: 667025.8 1.835034e-04
#> 4: 253985259.7 8.177107e-02
#> 5: 274129198.7 8.675243e-02
#> 6: 262194082.1 9.665513e-02
#> 7: 321728932.9 9.286884e-02
#> 8: 391613915.1 1.168782e-01
#> 9: 426538609.2 1.215089e-01
#> 10: 415505663.8 1.252873e-01
#> 11: 449201938.9 1.363737e-01
#> 12: 372073328.0 1.681376e-01
#> 13: 333066714.3 1.944387e-01
#> 14: 270782057.7 2.531493e-01
#> 15: 358211848.8 2.164940e-01
#> 16: 348242834.9 2.527084e-01
#> 17: 402462230.4 2.450020e-01
#> 18: 369366755.4 3.166778e-01
#> 19: 366351509.1 3.565763e-01
#> 20: 463783045.7 3.312479e-01
#> 21: 642996110.9 2.965359e-01
#> 22: 535744873.7 3.817711e-01
#> 23: 504337556.8 5.285368e-01
#> 24: 858712162.8 5.770031e-01
#> 25: 760483875.8 7.932718e-01
#> 26: 989734521.0 9.502916e-01
#> 27: 817491334.5 1.685580e+00
#> 28: 5652573520.7 1.294307e+01
#> 29: 0.0 NA
#> 30: 0.0 NA
#> se cv
#> <num> <num>fit_lr() 은 손해율 추정을 수행한다. 기본값으로 사용되는
단계 적응형(stage-adaptive) 방식 (method = "sa") 은
성숙점(maturity point) 이전에는 노출 기반 방식, 성숙점 이후에는 chain
ladder 를 적용한다. 전환 지점은 ATA 인자에서 그룹별로 탐지된
성숙점이다.
summary(lr)
#> cv_nm cohort latest ultimate reserve exposure_ult lr_latest
#> <char> <Date> <num> <num> <num> <num> <num>
#> 1: SUR 2023-04-01 2442597048 2442597048 0 2621263715 0.93183949
#> 2: SUR 2023-05-01 2423543638 2600462324 176918686 2447179856 1.06560740
#> 3: SUR 2023-06-01 3211045460 3634951626 423906166 3045660787 1.19909110
#> 4: SUR 2023-07-01 2552396709 3106052713 553656004 2859002910 1.08237572
#> 5: SUR 2023-08-01 2472997706 3159902325 686904619 2669412392 1.18159391
#> 6: SUR 2023-09-01 2014222417 2712676349 698453932 2893769135 0.95080886
#> 7: SUR 2023-10-01 2422172254 3464336723 1042164469 3094707504 1.14505029
#> 8: SUR 2023-11-01 2157147612 3350616805 1193469193 2879458974 1.18696133
#> 9: SUR 2023-12-01 2062030017 3510350121 1448320104 2843155654 1.24103978
#> 10: SUR 2024-01-01 1803809914 3316423447 1512613533 2974323108 1.11558443
#> 11: SUR 2024-02-01 1627213157 3293904272 1666691115 2661467254 1.22363541
#> 12: SUR 2024-03-01 1006624213 2212909862 1206285649 2483209943 0.88837590
#> 13: SUR 2024-04-01 707083237 1712964993 1005881756 2676093339 0.63405399
#> 14: SUR 2024-05-01 398857325 1069653556 670796231 2650183003 0.40197017
#> 15: SUR 2024-06-01 558855276 1654603718 1095748442 2653104690 0.62898298
#> 16: SUR 2024-07-01 423131371 1378042306 954910935 2758730502 0.51295338
#> 17: SUR 2024-08-01 457705980 1642689597 1184983617 2949332087 0.58596112
#> 18: SUR 2024-09-01 278007651 1166380310 888372659 2628969714 0.45517867
#> 19: SUR 2024-10-01 214811381 1027414214 812602833 2600171974 0.40289870
#> 20: SUR 2024-11-01 251273971 1400108561 1148834590 2558267999 0.56379157
#> 21: SUR 2024-12-01 322678179 2168358632 1845680453 2865484259 0.76337614
#> 22: SUR 2025-01-01 179253475 1403314539 1224061064 2811568885 0.51475151
#> 23: SUR 2025-02-01 100816665 1246593088 1145776423 3116396285 0.32204866
#> 24: SUR 2025-03-01 111279087 1859420120 1748141033 2859035735 0.48317257
#> 25: SUR 2025-04-01 55914454 1706798346 1650883892 2820900062 0.31249884
#> 26: SUR 2025-05-01 41578391 2113613662 2072035271 3170694661 0.27248380
#> 27: SUR 2025-06-01 14997314 1815491007 1800493693 2746665555 0.14942419
#> 28: SUR 2025-07-01 6232031 2701876633 2695644602 3705336068 0.07318336
#> 29: SUR 2025-08-01 0 2250325450 2250325450 2969197182 0.00000000
#> 30: SUR 2025-09-01 0 2371913171 2371913171 2995415555 0.00000000
#> cv_nm cohort latest ultimate reserve exposure_ult lr_latest
#> <char> <Date> <num> <num> <num> <num> <num>
#> lr_ult maturity_from proc_se param_se se cv
#> <num> <num> <num> <num> <num> <num>
#> 1: 0.9318395 9 0.0 0.0 0.0 0.0000000000
#> 2: 1.0626364 9 270023.8 278555.7 387951.2 0.0001491855
#> 3: 1.1934854 9 461673.6 481436.4 667025.8 0.0001835034
#> 4: 1.0864112 9 217960839.6 130390124.6 253985259.7 0.0817710719
#> 5: 1.1837445 9 235800277.9 139803599.9 274129198.7 0.0867524279
#> 6: 0.9374198 9 230925350.1 124174149.3 262194082.1 0.0966551289
#> 7: 1.1194391 9 276909538.1 163800531.1 321728932.9 0.0928688400
#> 8: 1.1636272 9 347646646.1 180286627.2 391613915.1 0.1168781564
#> 9: 1.2346669 9 379204803.4 195291838.6 426538609.2 0.1215088508
#> 10: 1.1150179 9 371903391.7 185291186.8 415505663.8 0.1252872772
#> 11: 1.2376272 9 406210629.2 191768888.6 449201938.9 0.1363737078
#> 12: 0.8911489 9 348109439.7 131371151.5 372073328.0 0.1681375886
#> 13: 0.6400991 9 316686848.8 103164315.5 333066714.3 0.1944387163
#> 14: 0.4036150 9 262671178.8 65778222.8 270782057.7 0.2531493082
#> 15: 0.6236481 9 342800640.3 103939643.9 358211848.8 0.2164940432
#> 16: 0.4995205 9 336548946.6 89486750.7 348242834.9 0.2527083771
#> 17: 0.5569700 9 387322897.0 109347246.8 402462230.4 0.2450019962
#> 18: 0.4436644 9 360265104.1 81491440.0 369366755.4 0.3166778043
#> 19: 0.3951332 9 358796880.9 74015042.1 366351509.1 0.3565762514
#> 20: 0.5472877 9 451728990.6 105050619.0 463783045.7 0.3312479179
#> 21: 0.7567163 9 619598522.3 171876903.1 642996110.9 0.2965358689
#> 22: 0.4991215 9 523388251.8 114399770.9 535744873.7 0.3817710561
#> 23: 0.4000111 9 701160983.1 151966055.9 717440176.1 0.5755207396
#> 24: 0.6503662 9 1008915827.7 229980336.9 1034795681.6 0.5565152653
#> 25: 0.6050545 9 1022367650.8 226433230.3 1047142598.3 0.6135127800
#> 26: 0.6666090 9 1151829299.7 274237738.8 1184025790.7 0.5601902618
#> 27: 0.6609800 9 1079112766.9 238225282.2 1105095312.1 0.6087032698
#> 28: 0.7291853 9 1349660358.1 349060403.8 1394068236.4 0.5159629494
#> 29: 0.7578902 9 1225790727.8 285878838.0 1258685671.0 0.5593349490
#> 30: 0.7918478 9 1250626904.3 295553950.3 1285075792.0 0.5417887162
#> lr_ult maturity_from proc_se param_se se cv
#> <num> <num> <num> <num> <num> <num>
#> se_lr cv_lr ci_lower ci_upper
#> <num> <num> <num> <num>
#> 1: 0.0000000000 0.0000000000 0.9318395 0.9318395
#> 2: 0.0001585299 0.0001491855 1.0623257 1.0629471
#> 3: 0.0002190086 0.0001835034 1.1930561 1.1939146
#> 4: 0.0888370064 0.0817710719 0.9122938 1.2605285
#> 5: 0.1026927123 0.0867524279 0.9824705 1.3850186
#> 6: 0.0906064271 0.0966551289 0.7598344 1.1150051
#> 7: 0.1039610149 0.0928688400 0.9156793 1.3231990
#> 8: 0.1360026028 0.1168781564 0.8970670 1.4301874
#> 9: 0.1500229537 0.1215088508 0.9406273 1.5287065
#> 10: 0.1396975543 0.1252872772 0.8412157 1.3888201
#> 11: 0.1687798105 0.1363737078 0.9068249 1.5684296
#> 12: 0.1498356307 0.1681375886 0.5974765 1.1848214
#> 13: 0.1244600513 0.1944387163 0.3961619 0.8840363
#> 14: 0.1021748526 0.2531493082 0.2033559 0.6038740
#> 15: 0.1350161002 0.2164940432 0.3590214 0.8882748
#> 16: 0.1262330027 0.2527083771 0.2521083 0.7469326
#> 17: 0.1364587705 0.2450019962 0.2895158 0.8244243
#> 18: 0.1404986727 0.3166778043 0.1682921 0.7190368
#> 19: 0.1408951072 0.3565762514 0.1189838 0.6712825
#> 20: 0.1812879049 0.3312479179 0.1919699 0.9026054
#> 21: 0.2243935241 0.2965358689 0.3169131 1.1965195
#> 22: 0.1905501503 0.3817710561 0.1256501 0.8725930
#> 23: 0.2302146808 0.5755207396 0.0000000 0.8512236
#> 24: 0.3619387016 0.5565152653 0.0000000 1.3597530
#> 25: 0.3712086835 0.6135127800 0.0000000 1.3326102
#> 26: 0.3734278817 0.5601902618 0.0000000 1.3985142
#> 27: 0.4023406891 0.6087032698 0.0000000 1.4495533
#> 28: 0.3762326036 0.5159629494 0.0000000 1.4665877
#> 29: 0.4239144772 0.5593349490 0.0000000 1.5887473
#> 30: 0.4290141947 0.5417887162 0.0000000 1.6327002
#> se_lr cv_lr ci_lower ci_upper
#> <num> <num> <num> <num>6단계 — 구조 변화 진단
detect_cohort_regime() 은 최근 코호트가 이전 코호트와
다르게 행동하는지 검사한다. 동질적 부분집합에 한하여 손해율 적합을
수행하기 위한 전처리 단계로 활용된다.
sub <- build_triangle(exp[cv_nm == "SUR"], group_var = cv_nm)
detect_cohort_regime(sub, K = 12, method = "ecp")
#> <CohortRegime>
#> method : ecp
#> value_var : clr
#> window (K) : elap_m 1, ..., 12
#> cohorts : 19 analysed (11 dropped)
#> regimes : 2
#> breakpoints : 24.03
#> PC1 / PC2 : 63.6% / 15.1%상세 설명은 vignette("regime-detection") 을
참고한다.
다음 단계
-
vignette("aggregation-frameworks")—build_triangle,build_calendar,build_total의 사용 시점 비교. -
vignette("loss-ratio-methods")—fit_lr()에서"sa"/"ed"/"cl"중 선택 기준. -
vignette("chain-ladder")—fit_cl()심층 해설 (Mack 분산, tail factor). -
vignette("triangle-diagnostics")—summary(),find_ata_maturity(), triangle 형식의 시각화. -
vignette("regime-detection")—detect_cohort_regime()을 통한 코호트 간 구조 변화 진단. -
vignette("backtest")—fit_cl또는fit_lr을 사용한 대각선 홀드아웃(holdout) 검증.