Optimal Reinsurance and Investment for a Jump Diffusion Risk Process under the CEV Model
Optimal Reinsurance and Investment for a Jump Diffusion Risk Process under the CEV Model
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DOI：
10.1080/10920277.2011.10597628
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发表时间：
2011-07
影响因子：
1.4
通讯作者：
Xiang Lin;Yanfang Li
中科院分区：
文献类型：
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作者：
Xiang Lin;Yanfang Li
摘要考虑了保险人的最优再保险投资问题，其盈余过程服从跳扩散模型。在我们的模型中，保险公司通过比例再保险转移部分保险索赔风险，并将盈余投资于一个由无风险资产和风险资产组成的“简化”金融市场。风险资产的动态是由一个恒定的方差弹性模型，以纳入条件异方差。保险人的目标是选择一个最优的再保险投资策略，使最终财富的期望指数效用最大化。我们调查的问题，使用Hamilton-Jacobi-Bellman动态规划方法。得到了最优再保险投资策略的显式表达式和相应的价值函数。数值算例说明了当模型参数变化时，最优投资再保险策略的变化。
Abstract We consider an optimal reinsurance-investment problem of an insurer whose surplus process follows a jump-diffusion model. In our model the insurer transfers part of the risk due to insurance claims via a proportional reinsurance and invests the surplus in a “simplified” financial market consisting of a risk-free asset and a risky asset. The dynamics of the risky asset are governed by a constant elasticity of variance model to incorporate conditional heteroscedasticity. The objective of the insurer is to choose an optimal reinsurance-investment strategy so as to maximize the expected exponential utility of terminal wealth. We investigate the problem using the Hamilton-Jacobi-Bellman dynamic programming approach. Explicit forms for the optimal reinsuranceinvestment strategy and the corresponding value function are obtained. Numerical examples are provided to illustrate how the optimal investment-reinsurance policy changes when the model parameters vary.