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.
Highlights
The investment and reinsurance are increasingly crucial issues for insurance companies
The essence of the mean-variance problem is to minimize the variance of the prospect while keep the expected prospect fixed, that is, the mean-variance problem is a constrained optimization problem as follows: Minimize J(u) = V arP [f ], EP [f ] = ξ, (1.1)
We focus on maximizing the insurance company’s monotone mean-variance preference utility rather than the classical mean-variance preference utility
Summary
The investment and reinsurance are increasingly crucial issues for insurance companies. Monotone mean-variance preference, Hamilton-Jacobi-Bellman-Isaacs equation, Monotone efficient frontier, Capital asset pricing model. Zhou and Li [28] studied the mean-variance problem in continuous-time market They introduced the linear-quadratic approach and obtained the optimal portfolio as well as the efficient frontier by solving a stochastic Riccati equation. The discounted terminal wealth process are considered They obtained the optimal portfolio and the value function when the coefficients are specified. For a large class of portfolio choice problem, [23] further proved that, when the risk assets are continuous semimartingales, the optimal portfolios and value functions of the classical mean-variance preference and the monotone mean-variance preference coincide. We consider financial assets, and insurance and reinsurance This is the first time that the monotone mean-variance objective is used for the optimal reinsurance problem. In Subsection 4.3, when only the financial market is considered, a monotone CAPM based on the monotone mean-variance preference is obtained
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