The investment and reinsurance game of insurers and reinsurers with default risk under CEV model

School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, P.R. China

^* Corresponding author: haowj0223@smail.swufe.edu.cn

Received: 18 January 2023
Accepted: 27 July 2023

Abstract

On the premise of considering the interests of insurance companies and reinsurance companies at the same time, this paper studies the investment and reinsurance game between them. Suppose that the compensation process faced by an insurance company is described by Brownian motion with drift. Insurance companies can purchase proportional reinsurance from reinsurance companies, and both companies can invest in a risk-free asset, a risky asset whose price process follows the constant elasticity of variance (CEV) model, and a defaultable bond. With the goal of maximizing the expected utility of weighted terminal wealth, the corresponding Hamilton–Jacobi–Bellman (HJB) equations are established and solved by using the principle of dynamic programming, and the analytical expressions of the equilibrium investment-reinsurance strategies of insurers and reinsurers are derived respectively. Finally, the influence of each model parameter on the equilibrium strategy is analyzed by numerical examples.