kernels.rereserve()

(n_draws, n_w) one-year CDR draws from simulated next-diagonal values.

Usage

Source

kernels.rereserve(
    fit,
    next_diagonal,
)

The second axis, and it is not a choice: the reserve is re-estimated with the volume-weighted chain ladder, which is the market convention and what R’s ChainLadder uses for its Mack CDR and its bootstrap CDR alike (getAvDFs(dfs, wghts) with the cumulative triangle as weights is the volume-weighted factor written out). Every generator therefore shares this one implementation, and a third-party diagonal - draws from any model that can predict next year’s cells - can be re-reserved by calling this directly.

next_diagonal[:, i] is origin i’s cumulative loss one year on, on the same basis as fit.cum. Closed origins are ignored (they have no next cell, so their CDR is identically zero); pass zeros there.

What happens, per draw:

  1. append the diagonal and re-run the chain ladder. Only the factors move, and each moves by exactly one new observation, because on a run-off staircase exactly one origin joins each development step next year:
f_j^{I+1} = (S_j f_j-hat + X_{i_j}) / (S_j + C_{i_j,j})

which is algebraically the volume-weighted factor recomputed on the extended triangle - the numerator S_j f_j-hat is sum_i C_{i,j+1} and the denominator is sum_i C_{i,j}, so adding the new pair to each is the refit; 2. re-project each origin’s ultimate off its new diagonal cell with the suffix product of the UPDATED factors; 3. CDR_i = C-hat_{i,J}^{I} - C-hat_{i,J}^{I+1}, so a positive draw is a reserve release.

Only f, s, latest, latest_dev and ultimate are read off the fit - the volume-weighted chain ladder and the triangle it came from. Mack’s sigma2 is not touched, which is why the ODP bootstrap can use the identical function.

ONE MACK ASSUMPTION SURVIVES HERE AND IT IS WORTH NAMING. Step 3 differences against fit.ultimate, the deterministic chain-ladder ultimate at time I. Under Mack that is exactly right and it is what makes E[CDR | D_I] = 0 - the draws are centred on zero, so E[CDR^2] (simulated_msep()) is the risk measure. Under a residual bootstrap the simulated diagonal’s mean is only approximately the chain-ladder projection, so the CDR draws carry a small bootstrap bias and the mean square about zero is not quite the variance. R makes the same distinction from the other side: its Mack CDR reports the analytic msep (about zero) while CDR.BootChainLadder reports sd() of the re-reserved amount (about its own mean). Report both when the generator is not mack.

Under a GALLERY generator the drift is not a nuisance at all - it is the model saying next year’s diagonal will land somewhere other than where the chain ladder puts it, which is most of what a separate model is FOR. It is still not part of a variance, so the same rule applies with more force: mean and sd separately, never E[CDR^2] alone.