On maximizing the expected terminal utility by investment and reinsurance
On maximizing the expected terminal utility by investment and reinsurance
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DOI：
10.3934/jimo.2008.4.801
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发表时间：
2008-11
影响因子：
1.3
通讯作者：
Lin Xu;Rongming Wang;Dingjun Yao
中科院分区：
文献类型：
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作者：
Lin Xu;Rongming Wang;Dingjun Yao
本文考虑了保险人在风险市场上投资并购买再保险的最优问题。保险人的盈余过程是一类带有随机保费收入的带扰动经典风险模型。风险市场的投资收益生成过程是一个漂移的布朗运动加复合泊松过程。在本文中的目标函数是最大化的期望效用财富的保险人在终端时间，说T$。通过求解与最优控制问题相关的Hamilton-Jacobi-Bellman方程，得到了最优策略和价值函数的封闭形式表达式，表明保险人同时购买投资和再保险的价值函数总是优于保险人只购买投资或再保险的价值函数.
In this paper, optimal problems for the insurer who can invest on risky market and purchase reinsurance are considered. The surplus process of the insurer is a kind of perturbed classical risk model with stochastic premium income. The investment return generating process of the risky market is a drifted Brownian motion plus a compound Poisson process. The objective function in this paper is to maximize the expected utility of wealth of the insurer at terminal time, say $T$. By solving the Hamilton-Jacobi-Bellman equations related to our optimal control problems, the closed form expression for optimal strategy and the value function is derived, which indicates that the value function for an insurer to purchase both investment and reinsurance is always better than the one for the insurer to purchase only either investment or reinsurance.