Mean-variance reinsurance and asset liability management with common shock via non-Markovian stochastic factors

Abstract

This paper explores a reinsurance and asset liability management problem in a factor model with dependent risks, considering economic factors as non-Markovian processes impacting the appreciation rate, volatility, and value of liabilities. It encompasses various stochastic volatility (SV) models like Hull-White, Heston, 3/2, and 4/2 models as special cases. The model addresses dependent risks through a common shock in claim number processes. The insurer's aim is to minimize variance in terminal net wealth while achieving a certain expected terminal net wealth, balancing reinsurance, new business, and asset allocation. The paper employs linear-quadratic (LQ) control and backward stochastic differential equation (BSDE) theory to derive both the efficient strategy and the efficient frontier. To illustrate our results, numerical examples are provided in two special cases, the 3/2 and 4/2 SV models.