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  

Optimal Investment and Combined Proportional-Excess of Loss Reinsurance with Stochastic Interest and Stochastic Volatility

作　　者：杨鹏[1] 林祥[2] 

机构地区：[1]西京学院基础部,陕西西安710123 [2]中南大学数学学院,湖南长沙410075

出　　处：《经济数学》2012年第1期42-46,共5页Journal of Quantitative Economics

基　　金：国家自然科学基金资助项目(10671212;10771216)

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.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- Jaeobi-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.

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 

分 类 号：F830[经济管理—金融学] O211.3[理学—概率论与数理统计]