Time-consistent mean-variance reinsurance-investment problem with long-range dependent mortality rate

TL;DR

This paper explores how long-range dependence in mortality rates affects time-consistent mean-variance reinsurance-investment strategies for life insurers, providing explicit controls and analyzing their uniqueness.

Contribution

It introduces a Volterra mortality model to incorporate LRD into RI strategies and derives explicit equilibrium controls under this framework.

Findings

LRD significantly influences equilibrium strategies.

Explicit controls are derived for different risk aversion cases.

Numerical results illustrate the impact of LRD on insurer strategies.

Abstract

This paper investigates the time-consistent mean-variance reinsurance-investment (RI) problem faced by life insurers. Inspired by recent findings that mortality rates exhibit long-range dependence (LRD), we examine the effect of LRD on RI strategies. We adopt the Volterra mortality model proposed in Wang et al.(2021) to incorporate LRD into the mortality rate process and describe insurance claims using a compound Poisson process with the intensity represented by stochastic mortality rate. Under the open-loop equilibrium mean-variance criterion, we derive explicit equilibrium RI controls and study the uniqueness of these controls in cases of constant and state-dependent risk aversion. We simultaneously resolve difficulties arising from unbounded non-Markovian parameters and sudden increases in the insurer's wealth process. We also use a numerical study to reveal the influence of LRD on equilibrium strategies.