损失厌恶下带有风险约束的委托投资组合模型

Delegated portfolio models with a risk constrain under loss aversion

在管理者呈损失厌恶的假设下,构建了带有风险约束的委托投资组合模型,研究委托投资管理中的最优投资问题.通过构造辅助函数将以条件风险价值为约束的委托投资组合问题转化为约束含有随机凸函数的随机优化问题,证明了最优策略的存在性.进而利用随机抽样方法构造了Monte Carlo罚函数算法,得到了近似最优投资策略,并证明了当样本容量足够大时近似最优投资策略几乎处处是原委托投资组合问题的最优策略.最后,给出了数值算例说明模型的有效性和管理者的损失厌恶对最优策略的影响.

Suppose that the manager is loss adverse the delegated portfolio model with a risk constraint is established in order to research the optimal investment problem in the delegated portfolio management. The delegated portfolio problem with the conditional value at risk as a constraint is transformed into a stochastic optimization with a stochastic convex function as a constraint by constructing the auxiliary function, and the existence of the optimal strategies is proved. Furthermore, the approximation optimal investment strategies are obtained based on the Monte Carlo penalty function algorithm constructed by using the random sampling method and are proved, to be almost everywhere the optimal strategies of the original delegated portfolio problem when the sample number is larger enough. Finally, the numerical examples are given to illustrate the effectiveness of the model and the effect of loss aversion of the manager on the optimal portfolio strategies.