含有信用风险的跳扩散市场的最优组合选择

Optimal Portfolio Selection for Containing Credit Risk in a Jump-Diffusion Market

假定投资者将其财富分配在这样两种风险资产中,一种是股票,价格服从跳跃扩散过程;一种是有信用风险的债券,其价格服从复合泊松过程.在均值方差准则下通过最优控制原理来研究投资者的最优投资策略选择问题,得到了最优投资策略及有效边界.最后通过数值例子分析了违约强度、债券预期收益率以及目标财富对最优投资策略的影响.

Assume that an investor can allocate his wealth dynamically between a risky stock,whose price follows a jump-diffusion process,and a risky bond,whose price is subject to negative jumps due to its credit risk.Its price contains discontinuous sample paths,so it is subject to the compound Poisson process.The optimal investment strategy under the mean-variance principle was studied by the stochastic control approach.The closed and explicit formulas for the optimal investment strategy and the efficient frontier were derived.Finally,the effects of default intensity,the expected rate of return and the wealth target on optimal investment strategy were analyzed by numerical examples.