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

Shumin Chen, Hailiang Yang and Yan Zeng

ASTIN Bulletin, 2018, vol. 48, issue 1, 413-434

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.

Date: 2018
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