Generalized Log-Normal Chain-Ladder

TL;DR

This paper develops an asymptotic distribution forecasting method for the log-normal chain-ladder model, accounting for estimation error and providing t-distribution based forecasts, supported by simulations and real data.

Contribution

It introduces a generalized log-normal chain-ladder model with an asymptotic theory that overcomes convolution difficulties and differs from existing models like the over-dispersed Poisson.

Findings

Forecast distributions follow t distributions under the asymptotic theory.

The model accounts for estimation error in distribution forecasting.

Simulations and empirical data support the theoretical results.

Abstract

We propose an asymptotic theory for distribution forecasting from the log normal chain-ladder model. The theory overcomes the difficulty of convoluting log normal variables and takes estimation error into account. The results differ from that of the over-dispersed Poisson model and from the chain-ladder based bootstrap. We embed the log normal chain-ladder model in a class of infinitely divisible distributions called the generalized log normal chain-ladder model. The asymptotic theory uses small $\sigma$ asymptotics where the dimension of the reserving triangle is kept fixed while the standard deviation is assumed to decrease. The resulting asymptotic forecast distributions follow t distributions. The theory is supported by simulations and an empirical application.