Fit loss ratio projection model

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

"sa" (default)

Uses exposure-driven (ED) estimation before maturity and chain ladder (CL) after maturity.

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.

"ed"

Exposure-driven for all development periods. All future increments are $g_k \cdot C^P_k$.

"cl"

Chain ladder for all development periods. Equivalent to classical Mack model.

In all cases, exposure is projected forward using chain ladder: $$\hat{C}^P_{i,k+1} = f^P_k \cdot \hat{C}^P_{i,k}$$

Usage

fit_lr(
  x,
  method = c("sa", "ed", "cl"),
  loss_var = "closs",
  exposure_var = "crp",
  loss_alpha = 1,
  exposure_alpha = 1,
  delta_method = c("simple", "full"),
  rho = 0,
  conf_level = 0.95,
  sigma_method = c("min_last2", "locf", "loglinear"),
  recent = NULL,
  regime_break = NULL,
  maturity_args = NULL,
  bootstrap = FALSE,
  B = 1000,
  seed = NULL
)

Arguments

x

An object of class "Triangle".

method

One of "sa", "ed", or "cl". Default is "sa".

loss_var

Cumulative loss variable. Default is "closs".

exposure_var

Cumulative exposure variable. Default is "crp".

loss_alpha

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

exposure_alpha

Numeric scalar for exposure chain ladder. Default is 1.

delta_method

Method for computing se_lr = SE(L/E). One of:

"simple" (default): se_lr = se_proj / exposure_proj, treats exposure as fixed.
"full": Full delta method with exposure uncertainty and loss-exposure correlation: $$\mathrm{Var}(L/E) \approx \frac{\mathrm{Var}(L)}{E^2} + \frac{L^2 \mathrm{Var}(E)}{E^4} - \frac{2 \rho L \mathrm{SE}(L) \mathrm{SE}(E)}{E^3}$$

rho

Numeric scalar in (-1, 1); assumed correlation between ultimate loss and ultimate exposure. Only used when delta_method = "full". Default is 0.

conf_level

Confidence level used for ci_lower/ci_upper in the cohort summary. Default is 0.95.

sigma_method

Sigma extrapolation method. One of "min_last2" (default), "locf", or "loglinear".

recent

Optional positive integer for estimation window. Default is NULL.

regime_break

Optional cohort cutoff for the regime break. Accepts: NULL (default, no filter), a single Date/character coercible to Date, a vector of dates (uses the latest), or a CohortRegime object (extracts the latest from $breakpoints). Behavior depends on method:

"sa": Hybrid filter. Pre-break 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 shift.
"ed", "cl": Simple cohort cut: all cohorts strictly before the break date are excluded from estimation.

maturity_args

A named list forwarded to find_ata_maturity(), or NULL (default) to skip maturity filtering. When method = "sa", this also determines the switch point between ED and CL. Pass list() to use all defaults.

bootstrap

Logical; if TRUE, parameter and process variance are derived via residual bootstrap rather than the analytical delta method. Default is FALSE.

B

Integer number of bootstrap replications. Used only when bootstrap = TRUE. Default is 1000.

seed

Optional integer seed for reproducible bootstrap. Default is NULL.

Value

An object of class "LRFit".

Examples

if (FALSE) { # \dontrun{
data(experience)
exp <- as_experience(experience)
tri <- build_triangle(exp[cv_nm == "SUR"], group_var = cv_nm)

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

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

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

Usage

Arguments

Value

See also

Examples