Optimal non-proportional reinsurance control and stochastic differential games

Michael Taksar and Xudong Zeng

Insurance: Mathematics and Economics, 2011, vol. 48, issue 1, 64-71

Abstract: We study stochastic differential games between two insurance companies who employ reinsurance to reduce risk exposure. We consider competition between two companies and construct a single payoff function of two companies' surplus processes. One company chooses a dynamic reinsurance strategy in order to maximize the payoff function while its opponent is simultaneously choosing a dynamic reinsurance strategy so as to minimize the same quantity. We describe the Nash equilibrium of the game and prove a verification theorem for a general payoff function. For the payoff function being the probability that the difference between two surplus reaches an upper bound before it reaches a lower bound, the game is solved explicitly.

Keywords: Non-proportional; reinsurance; HJB; equation; Ruin; probability; Stochastic; control; Stochastic; differential; game (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:48:y:2011:i:1:p:64-71

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