Disability insurance with collective health claims: A mean-field approach

TL;DR

This paper introduces a mean-field approach to model disability insurance with collective health claims, simplifying complex many-body problems into manageable equations for better pricing and prediction.

Contribution

It develops a novel mean-field approximation for collective health claims in disability insurance, enabling efficient computation and improved predictive accuracy.

Findings

Mean-field approximation performs well compared to Monte Carlo methods.

The approach provides a transparent pricing method for disability coverage.

The model captures both individual and collective health claim dynamics.

Abstract

The classic semi-Markov disability model is expanded with individual and collective health claims to improve its explanatory and predictive power -- in particular in the context of group experience rating. The inclusion of collective health claims leads to a computationally challenging many-body problem. By adopting a mean-field approach, this many-body problem can be approximated by a non-linear one-body problem, which in turn leads to a transparent pricing method for disability coverages based on a lower-dimensional system of non-linear forward integro-differential equations. In a practice-oriented simulation study, the mean-field approximation clearly stands its ground in comparison to na\"ive Monte Carlo methods.