Optimal investment and reinsurance of an insurer with model uncertainty

Xin Zhang and Tak Kuen Siu

Insurance: Mathematics and Economics, 2009, vol. 45, issue 1, 81-88

Abstract: We introduce a novel approach to optimal investment-reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment-reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton-Jacobi-Bellman-Isaacs (HJBI) solutions to the optimal investment-reinsurance problems and derive closed-form solutions to the problems.

Keywords: Optimal; investment; Proportional; reinsurance; Model; uncertainty; Stochastic; differential; game; Exponential; utility; Penalty; of; ruin; HJBI; equations (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (24)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:45:y:2009:i:1:p:81-88

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