A class of non-zero-sum stochastic differential investment and reinsurance games

Alain Bensoussan, Chi Chung Siu, Phillip Yam*, Hailiang Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

97 Citations (Scopus)

Abstract

In this article, we provide a systematic study on the non-zero-sum stochastic differential investment and reinsurance game between two insurance companies. Each insurance company’s surplus process consists of a proportional reinsurance protection and an investment in risky and risk-free assets. Each insurance company is assumed to maximize his utility of the difference between his terminal surplus and that of his competitor. The surplus process of each insurance company is modeled by a mixed regimeswitching Cramer–Lundberg diffusion approximation process, i.e. the coefficients of the diffusion risk
processes are modulated by a continuous-time Markov chain and an independent market-index process. Correlation between the two surplus processes, independent of the risky asset process, is allowed. Despite
the complex structure, we manage to solve the resulting non-zero sum game problem by applying the dynamic programming principle. The Nash equilibrium, the optimal reinsurance/investment, and the resulting value processes of the insurance companies are obtained in closed forms, together with sound
economic interpretations, for the case of an exponential utility function.
Original languageEnglish
Pages (from-to)2025 - 2037,
Number of pages13
JournalAutomatica
Volume50
DOIs
Publication statusPublished - Aug 2014
Externally publishedYes

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