Optimal dynamic excess-of-loss reinsurance and multidimensional portfolio selection

被引:0
|
作者
LiHua Bai
JunYi Guo
机构
[1] Nankai University,School of Mathematical Sciences
来源
Science China Mathematics | 2010年 / 53卷
关键词
exponential utility; Hamilton-Jacobi-Bellman equation; multiple risky asset investment; probability of ruin; excess-of-loss reinsurance; 93E20; 91B30;
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摘要
In this paper, the surplus process of the insurance company is described by a Brownian motion with drift. In addition, the insurer is allowed to invest in a risk-free asset and n risky assets and purchase excess-of-loss reinsurance. Under short-selling prohibition, we consider two optimization problems: the problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the probability of ruin. We first show that the excess-of-loss reinsurance strategy is always better than the proportional reinsurance under two objective functions. Then, by solving the corresponding Hamilton-Jacobi-Bellman equations, the closed-form solutions of their optimal value functions and the corresponding optimal strategies are obtained. In particular, when there is no risky-free interest rate, the results indicate that the optimal strategies, under maximizing the expected exponential utility and minimizing the probability of ruin, are equivalent for some special parameter. This validates Ferguson’s longstanding conjecture about the relation between the two problems.
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页码:1787 / 1804
页数:17
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