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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杨鹏 ,林祥 (1.西京学院 基础部陕西 西安7101232.中南大学 数学学院湖南 长沙410075) 
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
 
Optimal Investment and Combined Proportional-Excess of Loss Reinsurance with Stochastic Interest and Stochastic Volatility
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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