| 随机利率下有违约风险的最优投资组合 |
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| 引用本文： | 王利峰,孟庆欣.随机利率下有违约风险的最优投资组合[J].复旦学报(自然科学版),2005,44(3):382-387,394. |
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| 作者姓名： | 王利峰 孟庆欣 |
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| 作者单位： | 复旦大学,数学研究所,上海,200433;湖州师范学院,数学系,湖州,313000 |
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| 基金项目： | 国家自然科学基金;国家杰出青年科学基金;教育部科学技术研究项目 |
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| 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．
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| 关 键 词： | Cox-Ingersoll-Ross 随机利率 违约风险 随机控制 最优投资组合 |
| 文章编号： | 0427-7104(2005)03-0382-06 |
Optimal Investment with Stochastic Interest Rate and Default Risk |
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| WANG Li-feng,MENG Qing-xin.Optimal Investment with Stochastic Interest Rate and Default Risk[J].Journal of Fudan University(Natural Science),2005,44(3):382-387,394. |
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| Authors: | WANG Li-feng MENG Qing-xin |
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| Abstract: | 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. |
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| Keywords: | Cox-Ingersoll-Ross |
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