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

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). Volterra mortality model: actuarial valuation and risk management with long-range dependence. Insurance: Mathematics and Economics 96, 1–14] to incorporate LRD into the mortality rate process and describe insurance claims using a compound Poisson process with intensity represented by the 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. While the exiting literature suggests that LRD has a significant effect on longevity hedging, we find that reinsurance is a risk management strategy that is robust to LRD.