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STOCHASTIC DIFFERENTIAL GAMES BETWEEN TWO INSURERS WITH GENERALIZED MEAN-VARIANCE PREMIUM PRINCIPLE

Published online by Cambridge University Press:  19 January 2018

Shumin Chen ,
Hailiang Yang  and
Yan Zeng
Shumin Chen
Affiliation:
School of Management, Guangdong University of Technology, Guangzhou, China, E-Mail: chenshumin1@gmail.com
Hailiang Yang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, China, E-Mail: hlyang@hku.hk
Yan Zeng*
Affiliation:
Lingnan (University) College, Sun Yat-sen University, Guangzhou, China
*
E-Mail: zengy36@mail.sysu.edu.cn
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Abstract

We study a stochastic differential game problem between two insurers, who invest in a financial market and adopt reinsurance to manage their claim risks. Supposing that their reinsurance premium rates are calculated according to the generalized mean-variance principle, we consider the competition between the two insurers as a non-zero sum stochastic differential game. Using dynamic programming technique, we derive a system of coupled Hamilton–Jacobi–Bellman equations and show the existence of equilibrium strategies. For an exponential utility maximizing game and a probability maximizing game, we obtain semi-explicit solutions for the equilibrium strategies and the equilibrium value functions, respectively. Finally, we provide some detailed comparative-static analyses on the equilibrium strategies and illustrate some economic insights.

Keywords

Reinsurancegeneralized mean-variance premium principlenon-zero sum gameequilibrium strategyHamilton-Jacobi-Bellman equation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 413 - 434
Copyright
Copyright © Astin Bulletin 2018 

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