| 具有随机利率、随机变差的最优投资和联合比例-超额损失再保险 |
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| 引用本文：杨鹏 ，林祥.具有随机利率、随机变差的最优投资和联合比例-超额损失再保险[J].经济数学,2012,(1):42-46 |
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| 中文摘要:对跳-扩散风险模型，研究了最优投资和再保险问题.保险公司可以购买再保险减少理赔，保险公司还可以把盈余投资在一个无风险资产和一个风险资产上.假设再保险的方式为联合比例-超额损失再保险.还假设无风险资产和风险资产的利率是随机的，风险资产的方差也是随机的.通过解决相应的Hamilton-Jacobi-Bellman(HJB)方程，获得了最优值函数和最优投资、再保险策略的显示解.特别的，通过一个例子具体的解释了得到的结论. |
| 中文关键词:随机控制 Hamilton-Jacobi-Bellman(HJB) 跳-扩散风险模型 随机利率；随机变差 |
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| Optimal Investment and Combined Proportional-Excess of Loss Reinsurance with Stochastic Interest and Stochastic Volatility |
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| Abstract:For jump-diffusion risk model, we considered the problem of optimal investment and reinsurance. The insurance company can purchase reinsurance for claims and invest the surplus in a risk-free asset and a risky asset. We assume that the form of reinsurance is a combined proportional-excess of loss reinsurance. We also assume that the risk-free asset has stochastic interest and the risky asset has both stochastic interest and stochastic volatility. By solving the corresponding Hamilton-Jacobi-Bellman(HJB) equation, the closed-form expressions for the value function as well as the optimal investment and reinsurance policy were obtained. Especially, through an example we interpreted the results more specifically. |
| keywords:stochastic control Hamilton-Jacobi-Bellman(HJB) equation Jump-diffusion risk model stochastic interest Stochastic volatility |
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