One-year reserve risk including a tail factor: closed formula and bootstrap approaches

TL;DR

This paper compares simulation and bootstrap methods for measuring one-year reserve risk, incorporating a tail factor, and provides closed-form formulas and empirical validation for these approaches.

Contribution

It introduces a bootstrap approach that includes tail factor modeling and proves its equivalence to existing analytical formulas for reserve risk prediction error.

Findings

Bootstrap method with tail factor matches analytical variance

Closed-form expressions for prediction error including tail factor

Numerical example demonstrating method effectiveness

Abstract

In this paper, we detail the main simulation methods used in practice to measure one-year reserve risk, and describe the bootstrap method providing an empirical distribution of the Claims Development Result (CDR) whose variance is identical to the closed-form expression of the prediction error proposed by W\"uthrich et al. (2008). In particular, we integrate the stochastic modeling of a tail factor in the bootstrap procedure. We demonstrate the equivalence with existing analytical results and develop closed-form expressions for the error of prediction including a tail factor. A numerical example is given at the end of this study.