Optimal reinsurance and investment with a common shock and a random exit time

¹ School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, P.R. China
² Center for Optimization Technique and Quantitative Finance, Xi’an International Academy for Mathematics and Mathematical Technology, Xi’an 710049, P.R. China
³ School of Mathematics, Xi’an University of Finance and Economics, Xi’an 710100, P.R. China
⁴ School of Government, Peking University, Beijing 100871, P.R. China

^* Corresponding author: zchen@mail.xjtu.edu.cn.

Received: 20 April 2022
Accepted: 25 March 2023

Abstract

Under the mean-variance framework, we study the continuous-time optimal reinsurance and investment problem with a common shock and a random exit time. To describe the influence of the common shock, we propose a new interdependence mechanism between the insurance market and the financial market. It can reflect both the impact of the occurrence of a common shock and its influence degree on the two markets. Both the termination times of reinsurance and investment are random, and the random exit time is affected simultaneously by exogenous and endogenous random events. The insurer’s objective is to minimize the variance of her terminal wealth under a given level of expected terminal wealth. We derive the explicit optimal reinsurance-investment strategy by employing stochastic optimal control and Lagrange duality techniques. The influences of the market interdependence and the random exit time on the optimal strategy are demonstrated through numerical experiments. The results reveal some meaningful phenomena and provide insightful guidance for reinsurance and investment practice in reality.