Continuous-time modeling and bootstrap for Schnieper's reserving

TL;DR

This paper introduces a continuous-time stochastic model for claims reserves based on Schnieper's approach, incorporating a bootstrap method for predictive distribution estimation that respects reserve constraints.

Contribution

It develops a novel continuous-time framework and bootstrap technique for claims reserving, aligning with Schnieper's model and improving predictive accuracy and constraint adherence.

Findings

The bootstrap method effectively estimates the full distribution of reserves.

The model accounts for asymmetry and non-negativity naturally.

Case study demonstrates improved reserve prediction accuracy.

Abstract

We revisit Schnieper's model, which decomposes incurred but not reported (IBNR) reserves into two components: reserves for newly reported claims (true IBNR) and reserves for changes over time in the estimated cost of already reported claims (IBNER). We propose a continuous-time stochastic model for the aggregate claims process, driven by a random Poisson measure for the arrival of newly reported claims and by Brownian motion for the cost fluctuations of reported claims. This framework is consistent with the key assumptions of Schnieper's original approach. Within this setting, we develop a bootstrap method to estimate the full predictive distribution of claims reserves. Our approach naturally accounts for asymmetry, ensures non-negativity, and respects intrinsic bounds on reserves, without requiring additional assumptions. We illustrate the method through a case study and compare it with alternative stochastic techniques based on Schnieper's model.