Fit loss ratio projection model

Unified interface for loss ratio projection from a "Triangle" object. Five projection methods are available:

"ed" (default)

Exposure-driven for all development periods. All future increments are $g_k \cdot C^P_k$. Unconditional safe baseline – no maturity dependency, robust under early-dev ATA volatility.

"cl"

Chain ladder for all development periods. Equivalent to the classical Mack (1993) recursion.

"sa"

Stage-adaptive composition: ED before maturity, CL after maturity. Requires maturity detection (2-pass), uses age-to- age factors only once they have stabilised.

Before maturity: age-to-age factors are volatile, so exposure-driven projection $\Delta C^L = g_k \cdot C^P_k$ anchors the estimate to premium volume.
After maturity: age-to-age factors are stable, so chain ladder projection $C^L_{k+1} = f_k \cdot C^L_k$ preserves the cohort's observed level.

"bf"

Bornhuetter-Ferguson: blends the chain-ladder ultimate with an external prior loss ratio by the emergence fraction. Requires a prior argument, passed through ....

"cc"

Cape Cod: like "bf", but the prior loss ratio is estimated by pooling the data rather than supplied externally.

In all cases, premium is projected forward to ultimate; the point projection is identical under premium_method = "ed" or "cl" (they differ only in the variance recursion).

This function is the composition layer over fit_loss() and fit_premium(): it delegates loss projection to fit_loss(), retrieves the embedded PremiumFit, and composes the loss-ratio point + variance via the delta method (se_method = "fixed" or "delta"). See ARCHITECTURE.md for the layered design.

Usage

fit_ratio(
  x,
  method = c("ed", "cl", "sa", "bf", "cc"),
  loss_alpha = 1,
  loss_regime = NULL,
  premium_method = c("ed", "cl"),
  premium_alpha = 1,
  premium_regime = NULL,
  sigma_method = c("locf", "min_last2", "loglinear", "mack", "none"),
  recent = NULL,
  maturity = "auto",
  tail = FALSE,
  se_method = c("fixed", "delta"),
  rho = 0.95,
  conf_level = 0.95,
  bootstrap = NULL,
  B = 999L,
  seed = NULL,
  ...
)

Arguments

x

An object of class "Triangle". The standardized "loss" and "premium" columns are used (as_triangle() produces these).

method

One of "ed" (default), "cl", "sa", "bf", or "cc" – the loss-side projection method, forwarded to fit_loss(). "bf" and "cc" require their prior arguments (prior, etc.) supplied through ....

loss_alpha

Numeric scalar controlling the variance structure for loss estimation. Default is 1.

loss_regime

Optional regime specification for the loss-side filter. Accepts four input types:

NULL (default): No regime filter.
Regime object: Use as-is. Typically built via detect_regime() or regime_at().
"auto": Detect regime internally via detect_regime(x) on the input triangle.
Function / closure: A user-supplied function taking the triangle and returning a Regime object (or NULL).

Behavior depends on method:

"sa": Hybrid filter. Pre-change cohorts are dropped only for development periods at or before the maturity point (ED phase); post-maturity (CL) cells use the recent-diagonal window across all cohorts. This preserves CL stability while protecting the ED intensities from a regime change.
"ed", "cl": Simple cohort cut: all cohorts strictly before the change date are excluded from estimation.

premium_method

One of "ed" (default) or "cl". Forwarded to fit_premium() when constructing the premium projection.

premium_alpha

Numeric scalar for premium chain ladder. Default is 1.

premium_regime

Premium-side regime specification. Same four input types as loss_regime (NULL / Regime / "auto" / function). Default NULL – premium is fit on the full triangle independently of loss_regime (no lazy default). Set explicitly when the regime shift affects premium accrual too.

sigma_method

Method used to extrapolate sigma for links where it cannot be estimated. One of "locf" (default), "min_last2", "loglinear", "mack", or "none". "mack" applies the Mack (1993, Appendix B) tail estimator to the last unestimated link only, falling back to LOCF for any earlier ones with a warning. "none" performs no extrapolation; sigma stays NA and downstream variance terms drop those links via finite-value guards. Passed to .extrapolate_sigma_ata().

recent

Optional positive integer for estimation window. Default is NULL.

maturity

Optional maturity specification. Accepts four input types:

NULL: No maturity filter. Disables SA-mode switch detection.
Maturity object: Use as-is. Typically built via detect_maturity() or maturity_at().
"auto" (default): Detect maturity internally via detect_maturity(x) on the input triangle.
Function / closure: A user-supplied function taking the triangle and returning a Maturity object (e.g. from maturity_spec()) for deferred custom-config detection.

When method = "sa", this also determines the switch point between ED and CL phases.

tail

Tail factor for the loss-side projection, forwarded to fit_loss(). FALSE (default) applies none; TRUE estimates a log-linear tail factor; a numeric value is used directly.

se_method

Method for computing ratio_se = SE(L/P). One of:

"fixed" (default): Premium treated as fixed (non-random). $\mathrm{SE}(L/P) = \mathrm{SE}(L) / P$. Strictly, this is the delta method with Var(P) = 0 and Cov(L,P) = 0, i.e., a degenerate case under the assumption that premium is known.
"delta": Full delta method including premium uncertainty and the loss-premium correlation rho: $$\mathrm{Var}(L/P) \approx \frac{\mathrm{Var}(L)}{P^2} + \frac{L^2 \mathrm{Var}(P)}{P^4} - \frac{2 \rho L \mathrm{SE}(L) \mathrm{SE}(P)}{P^3}$$

rho

Numeric scalar in (-1, 1); assumed correlation between ultimate loss and ultimate premium. Only used when se_method = "delta". Default is 0.95, matching the strong positive correlation typically observed between cumulative loss and cumulative premium in long-tail health portfolios (analogous to the paid/incurred correlation used in Munich chain ladder).

conf_level

Confidence level used for ratio_ci_lo/ratio_ci_hi in the cohort summary. Default is 0.95.

bootstrap

Bootstrap configuration. Five forms accepted:

NULL (default): Auto-resolved by method: bootstrap for "sa"/"ed", analytical for "cl"/"bf"/"cc".
TRUE / FALSE: Back-compat with the legacy logical arg. TRUE triggers "auto"; FALSE disables.
"auto": Internal bootstrap() call on the loss triangle with defaults (type = "analytical", process = "normal", target = "loss").
BootstrapTriangle: Pre-built object from bootstrap(). Must have meta$target == "loss".
Function function(tri) -> BootstrapTriangle: Lazy spec invoked on the input Triangle (leakage-safe for backtest()).

Premium is held at observed values during the bootstrap (loss-only convention). ratio_se is recomputed from the bootstrap-derived loss_total_se via .compute_ratio_se(), combined with the premium-side SE per se_method ("fixed" ignores premium SE; "delta" uses premium_total_se from the inner fit_premium() plus rho correlation).

B

Integer number of bootstrap replications. Used only when bootstrap resolves to "auto". Default is 999.

seed

Optional integer seed for reproducible bootstrap. Default is NULL.

...

Additional arguments forwarded to fit_loss() and its worker – notably prior (and related arguments) when method = "bf" or "cc".

Value

An object of class "RatioFit".

Examples

if (FALSE) { # \dontrun{
data(experience)
tri <- as_triangle(
  experience[coverage == "surgery"],
  groups   = "coverage",
  cohort   = "uy_m",
  calendar = "cy_m",
  loss     = "incr_loss",
  premium = "incr_premium"
)

# Stage-adaptive (default): ED before maturity, CL after
ratio_sa <- fit_ratio(tri, method = "sa")
summary(ratio_sa)
plot(ratio_sa)

# Pure exposure-driven for all development periods
ratio_ed <- fit_ratio(tri, method = "ed")

# Pure chain ladder (Mack-style) for all development periods
ratio_cl <- fit_ratio(tri, method = "cl")
} # }

Usage

Arguments

Value

See also

Examples