带跳的具有卖空限制的证券投资组合选择问题  

Mean-variance portfolio selection with no-shorting constraints when stock prices follow jump-diffusion process

作　　者：薛赟[1] 刘宣会[1] 袁敏[1] 

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2010年第1期46-53,共8页Basic Sciences Journal of Textile Universities

摘　　要：研究了股票价格服从跳跃扩散过程的具有限制卖空约束的均值-方差投资组合选择问题.首先建立一个最优随机LQ问题,由于此问题具有限制卖空约束,因此传统的Riccati方程理论就不再适用,另外与之相关的HJB方程也不存在光滑解.通过2个Riccati方程构建一个连续函数,并证明这个函数就是HJB方程的粘性解.最后通过解Riccati方程得到原始均值-方差问题的有效边界和最优投资策略.It is studied that mean-variance portfolio selection in continuous-time under the constraints that shortselling of stocks is prohibited when stock prices follow jump-diffusion process. A stochastic optimal linear-quadratic （LQ） control problem is formulated. Due to the no-shorting restriction, the usual Riccati equation approach was not apphed directly. In addition, the corresponding HJB equation inherently has no smooth solution. A continuous function via two Riccati equation is constructed, and it is proved that this function is a viscosity solution to the HJB equation. The efficient frontier and optimal investment strategies for the original mean-variance problena are obtained by solving Riccati equations.

关 键 词：跳跃扩散过程 HJB方程 限制卖空 粘性解 有效边界 

分 类 号：O221[理学—运筹学与控制论]