Optimal investment and reinsurance of an insurer with model uncertainty Zhang, Xin; Siu, Tak Kuen; Macquarie University. Department of Actuarial Studies

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Zhang, Xin ; Siu, Tak Kuen ; Macquarie University. Department of Actuarial Studies
HJBI equations; Proportional reinsurance; Exponential utility
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. 8 page(s)
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