财富约束条件下损失厌恶投资者的动态投资组合选择

Dynamic portfolio selection for loss-averse investors with wealth constraints

在完全市场框架下,假定投资者是损失厌恶的,研究了财富非负和带有基准下限约束条件下一般情形的动态投资组合选择模型.利用鞅方法,分别获得了投资者的最优期末财富水平,证明了相应的拉格朗日乘子的存在唯一性.分析了这些解的性质,并且和传统风险厌恶投资者的最优解进行了比较.最后讨论了一个具体例子,给出了最优财富过程和最优投资策略的解析表达式.通过理论的结果和图形的显示,可以发现损失厌恶投资者的最优财富随着市场状态的变化会出现突变,如果考虑基准下限约束,则其投资策略相对保守,可以避免由于突变所造成的大的损失.

This paper studies a general dynamic portfolio selection model for loss-averse investors with wealth constraints in a complete market. By applying the martingale approach, we derive the optimal terminal wealth of the investors with or without the benchmark floor constraints respectively. Simultane- ously, the existence and uniqueness of the corresponding Lagrange multiplier are proved. We analyze the properties of these solutions, and compare them to that of the general risk-avers investors. An example with a two-piece power utility is presented to obtain the optimal wealth processes and the investment strategies by the replicating technique. By the theories and figures, it can be seen that the optimal wealth of the loss-averse investors has discontinuous jump with the change of market circumstances. If considering the benchmark floor constraint, then their investment strategies are relatively conservative and great losses can be avoided.