Optimal reinsurance and investment strategies for an insurer under monotone mean-variance criterion

School of Mathematical Sciences, Nankai University, Tianjin, 300071, P.R. China

^* Corresponding author: jyguo@nankai.edu.cn

Received: 7 January 2020
Accepted: 28 July 2021

Abstract

This paper considers the optimal investment-reinsurance problem under the monotone mean-variance preference. The monotone mean-variance preference is a monotone version of the classical mean-variance preference. First of all, we reformulate the original problem as a zero-sum stochastic differential game. Secondly, the optimal strategy and the optimal value function for the monotone mean-variance problem are derived by the approach of dynamic programming and the Hamilton-Jacobi-Bellman-Isaacs equation. Thirdly, the efficient frontier is obtained and it is proved that the optimal strategy is an efficient strategy. Finally, the continuous-time monotone capital asset pricing model is derived.