Chain ladder method: Bayesian bootstrap versus classical bootstrap

TL;DR

This paper introduces a novel distribution-free Bayesian approach using ABC, MCMC, and bootstrap to estimate claims reserving models, providing a flexible alternative to classical methods.

Contribution

It develops a new distribution-free Bayesian bootstrap methodology for claims reserving, enabling parameter and predictive distribution estimation without parametric assumptions.

Findings

The Bayesian bootstrap approach produces comparable estimates to classical methods.

The methodology effectively estimates predictive distributions and capital requirements.

Results demonstrate the flexibility and robustness of the distribution-free Bayesian framework.

Abstract

The intention of this paper is to estimate a Bayesian distribution-free chain ladder (DFCL) model using approximate Bayesian computation (ABC) methodology. We demonstrate how to estimate quantities of interest in claims reserving and compare the estimates to those obtained from classical and credibility approaches. In this context, a novel numerical procedure utilising Markov chain Monte Carlo (MCMC), ABC and a Bayesian bootstrap procedure was developed in a truly distribution-free setting. The ABC methodology arises because we work in a distribution-free setting in which we make no parametric assumptions, meaning we can not evaluate the likelihood point-wise or in this case simulate directly from the likelihood model. The use of a bootstrap procedure allows us to generate samples from the intractable likelihood without the requirement of distributional assumptions, this is crucial to the ABC framework. The developed methodology is used to obtain the empirical distribution of the DFCL model parameters and the predictive distribution of the outstanding loss liabilities conditional on the observed claims. We then estimate predictive Bayesian capital estimates, the Value at Risk (VaR) and the mean square error of prediction (MSEP). The latter is compared with the classical bootstrap and credibility methods.