Skip to contents

Find the development period at which the loss ratio estimate stabilises

Source: R/lr-convergence.R
find_lr_convergence.Rd

Identify the first valuation \(k^{**}\) from which the projected loss ratio is predictively stable, in the sense of the paper's Section 11 \(k^{**}\) criterion:

$$k^{**} = \min\{v \in [k^*, V - M] : R_v < c \cdot \hat{SE}^{param}_v \text{ and } \hat{D}_v < \tau, \text{ for } M \text{ consecutive valuations}\}$$

where \(R_v\) is the predictive revision in the projected loss ratio when calendar diagonal \(D_v\) is added, \(\hat{SE}^{param}_v\) is the parameter component of the Mack standard error of the projection, \(\hat{D}_v\) is the robust cross-cohort dispersion of incremental loss ratios at \(v\), and \(k^*\) is the age-to-age maturity point from find_ata_maturity().

Both clauses guard against complementary failure modes: \(R_v < c \cdot \hat{SE}^{param}_v\) requires the projection to stop responding to new diagonals at a scale-relevant magnitude; \(\hat{D}_v < \tau\) requires cross-cohort agreement on the incremental-LR level (inertia-free per-period quantity).

This function corresponds to the paper's convergence point \(k^{**}\), paired with \(k^*\) (maturity point).

Usage

find_lr_convergence(
  triangle,
  fit_fn = fit_lr,
  c = 0.5,
  tau = 0.15,
  M = 3L,
  k_star = NULL,
  holdout_max = NULL,
  min_n_cohorts = 5L,
  ...
)

Arguments

triangle

A Triangle object (typically from build_triangle()).

fit_fn

Fitting function used to project. Default fit_lr. fit_cl is also accepted but fit_lr is recommended because it exposes both loss and exposure projections required for portfolio LR.

c

Multiplier on \(\hat{SE}^{param}_v\). Default 0.5.

tau

Upper bound on \(\hat{D}_v\). Default 0.15.

M

Required run length of consecutive passing periods. Default 3L.

k_star

Pre-computed maturity point. When NULL, computed via find_ata_maturity() applied to a clr-based ATA.

holdout_max

Maximum holdout depth used for the rolling backtest. When NULL, set to max(M, floor((V - k_star) / 2)).

min_n_cohorts

Minimum number of cohorts required to compute \(\hat{D}_v\). Default 5L.

...

Additional arguments forwarded to fit_fn.

Value

An object of class LRConvergence (named list) containing the detected k_conv, the candidate sequence v, and the diagnostic sequences R_v, SE_param_v, D_v, pass_v. Metadata is carried on attributes (group_var, value_var, fit_fn_name).

See also

find_ata_maturity(), backtest(), fit_lr()