Stochastic differential games between two insurers with generalized mean-variance premium principle

Shumin Chen, Hailiang Yang, Yan Zeng*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

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 semiexplicit 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.
Original languageEnglish
Pages (from-to)413-434
Number of pages22
JournalASTIN Bulletin
Volume48
Issue number1
DOIs
Publication statusPublished - 15 Jan 2018
Externally publishedYes

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