基于CaR风险约束的动态投资组合模型

Dynamic Portfolio Model under a Capital at Risk Constraint

研究了带有风险约束的动态投资组合优化问题.在Black-Scholes型金融市场下,引入了在险资本(Captical at risk,CaR)风险约束,与以往文献的风险约束仅仅施加于终端时点不同,该模型将风险约束施加于每一个交易区间.即利用条件信息不断地对风险进行重新评估,从而对投资决策连续地施加影响.利用动态规划技术和优化理论,在合理的假定下,从理论上对问题进行了分析,给出了最优投资策略的显式表达式,并与无风险约束情形进行了比较.最后给出了一些数值例子进行说明.

We investigate dynamic portfolio selection problem. In a Black-Scholes setting, a capital at risk constraint is imposed. Making use of condition information, the risk of portfolio is reevaluated dynamically to influence the investment decision, rather than only at the terminal date like previous papers. Under the reasonable assumption, we apply the dynamic programming technique and optimal theory to derive the explicit solution of the optimal strategies, and numerical examples are presented.