随机利率下有违约风险的最优投资组合  

Optimal Investment with Stochastic Interest Rate and Default Risk

作　　者：王利峰[1] 孟庆欣[2] 

机构地区：[1]复旦大学数学研究所,上海200433 [2]湖州师范学院数学系,湖州313000

出　　处：《复旦学报（自然科学版）》2005年第3期382-387,394,共7页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金资助项目(101310310);国家杰出青年科学基金资助项目(10325101);国家教育部科学基金资助项目(20030246004)

摘　　要：通过随机最优控制方法讨论随机利率下有违约风险的最优投资组合问题,用约化形式方法对违约风险建模,假定利率和信用利差都服从Cox Ingersoll Ross模型,将最优投资组合问题看作一个三维的随机最优控制问题,给出了相应的Hamilton Jacobi Bellman方程的显式解和最优投资策略.The following optimal investment problem is considered.The financial market consists of a savings account,default-free zero coupon bonds,defaultable zero coupon bonds and stocks.An investor can invest in them without any restrict and tries to maximize the expected utility from his terminal wealth.The default risk is modeled in a reduced form approach.The interest rate and the credit spread are assumed to follow the Cox-Ingersoll-Ross model.The optimal investment problem is treated as an optimal control problem for a three-dimensional stochastic differential system.The associated Hamilton-Jacobi-Bellman equation is solved explicitly,and the optimal portfolio is also given in a closed form.

关 键 词：Cox—Ingersoll-Ross 随机利率 违约风险 随机控制 最优投资组合 

分 类 号：O211.6[理学—概率论与数理统计]