Optimal investment and reinsurance policies for the Cram{\'e}r-Lundberg risk model under monotone mean-variance preference

Autor:	Li, Bohan, Guo, Junyi, Tian, Linlin
Rok vydání:	2022
Předmět:	Mathematics - Optimization and Control 49L20 93E20 91B30
Druh dokumentu:	Working Paper
Popis:	In this paper, an optimization problem for the monotone mean-variance(MMV) criterion is considered in the perspective of the insurance company. The MMV criterion is an amended version of the classical mean-variance(MV) criterion which guarantees the monotonicity of the utility function. With this criterion we study the optimal investment and reinsurance problem which is formulated as a zero-sum game between the insurance company and an imaginary player. We apply the dynamic programming principle to obtain the corresponding Hamilton-Jacobi-Bellman-Isaacs(HJBI) equation. As the main conclusion of this paper, by solving the HJBI equation explicitly, the closed forms of the optimal strategy and the value function are obtained. Moreover, the MMV efficient frontier is also provided. At the end of the paper, a numerical example is presented. Comment: 22 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.01056 Zobrazit plný text záznamu View this record from Arxiv