Continuous-time modeling and bootstrap for chain-ladder reserving

TL;DR

This paper introduces a continuous-time stochastic differential equation model for chain-ladder claims reserving, along with a bootstrap method to estimate reserve distribution, capturing asymmetry and non-negativity without extra assumptions.

Contribution

It develops a novel continuous-time framework and bootstrap approach for claims reserving, improving upon traditional models like Mack's by inherently handling asymmetry and non-negativity.

Findings

The proposed model accurately estimates claims reserves.

Bootstrap method effectively captures reserve distribution.

Comparative analysis shows advantages over Mack's model.

Abstract

We revisit the famous Mack's model which gives an estimate for the conditional mean squared error of prediction of the chain-ladder claims reserves. We introduce a stochastic differential equation driven by a Brownian motion to model the accumulated total claims amount for the chain-ladder method. Within this continuous-time framework, we propose a bootstrap technique for estimating the distribution of claims reserves. It turns out that our approach leads to inherently capturing asymmetry and non-negativity, eliminating the necessity for additional assumptions. We conclude with a case study and comparative analysis against alternative methodologies based on Mack's model.