风险模型的最优投资和再保险  

Optimal investment and reinsurance for risk model

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：《西北师范大学学报（自然科学版）》2012年第3期24-31,共8页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10671212;10771216)

摘　　要：研究了跳-扩散风险模型和扩散风险模型的最优投资和再保险问题.在这两个风险模型中,保费收入都是复合泊松过程,且假设投资者可以投资一个无风险资产和一个跳项是复合泊松过程的跳-扩散过程的风险资产.对于扩散风险模型,则考虑投资具有随机利率和随机波动的资产.对这两个模型,以盈余终值的期望效用达到最大为最优准则获得了最优策略和值函数的表达式.The optimal investment and reinsurance policy are studied for jump-diffusion risk model and diffusion risk model. In the two risk models, premium income is modeled by a compound Poisson process, it is assumed that the investor can invest in a risk-free asset and a risky asset. The risky asset follows a jump-diffusion process which modeled by a compound Poisson process. In diffusion risk model, both stochastic interest rate and stochastic volatility are discussed. For the two models, the closed form expressions of the strategy and the value function are obtained, which are optimal in the sense of maximizing the expected utility terminal.

关 键 词：跳-扩散风险模型 扩散风险模型 HAMILTON-JACOBI-BELLMAN方程 随机保费 随机利率 随机波动 

分 类 号：O211.63[理学—概率论与数理统计] O232[理学—数学]