Bivariate phase-type distributions for experience rating in disability insurance

TL;DR

This paper introduces bivariate phase-type distributions for experience rating in disability insurance, linking mixed Poisson models with Markov chain frameworks, and demonstrates improved rate estimation through dependency modeling.

Contribution

It develops new multivariate mixed Poisson models with phase-type distributions and applies EM algorithms for maximum likelihood estimation in disability insurance context.

Findings

Dependency modeling improves rate estimates

EM algorithms effectively estimate model parameters

Numerical study confirms enhanced predictive performance

Abstract

In this paper, we consider the problem of experience rating within the classic Markov chain life insurance framework. We begin by establishing a link between mixed Poisson distributions and the problem of pricing group disability insurance contracts that exhibit heterogeneity. We focus on shrinkage estimation of disability and recovery rates, taking into account sampling effects such as right-censoring. We then investigate some specific multivariate mixed Poisson models with mixing distributions encompassing independent Gamma, hierarchical Gamma, and multivariate phase-type. In particular, we demonstrate how maximum likelihood estimation for these models can be performed using expectation-maximization algorithms, which might be of independent interest. Finally, we showcase the practicality of the proposed shrinkage estimators through a numerical study based on simulated yet realistic insurance data. Our findings highlight that by allowing for dependency between latent group effects, estimates of recovery and disability rates mutually improve, leading to enhanced predictive performance.