基于凸概度分布簇下WCVaR模型的有限逼近性

Finite Approximation of the Worst Conditional Value-at-Risk Model under the Convex Probability Distribution Cluster

如何求解实际问题中Worst条件风险值模型是一个非常困难的问题,研究了凸概率分布簇下的WCVaR(Worst Conditional Value-at-Risk)模型等价性及其在序列分布簇下的有限逼近性,根据概率分布簇的VaR测度值,定义了WCVaR风险测度值和对应的WCVaR模型,证明了WCVaR模型等价一个另一个数学规划问题求解.在一定条件下,证明了在损失有界情形用有限个分布簇就可以足够近似计算WCVaR模型的最优解,因此,对于解决稳健型条件风险值模型具重要的实际价值.

How to solve the worst conditional value at risk model in practical problems is a very difficult problem under the convex probability distribution cluster. In this paper, the equivalence of WCVaR(Worst Conditional Value-at-Risk) model under the convex probability distribution cluster and its properties under the sequence distribution cluster are studied.According to the VaR measure under the convex probability distribution cluster, the WCVaR optimization problem is defined by the WCVaR risk measurement. It is proved that the WCVaR optimization problem is equivalent to solve a nonlinear optimization problem.Under certain conditions, we prove that the optimal solution of the WCVaR problem can be approximated by a finite distributions cluster. Therefore, it has important practical value for solving the conditional conditional value at risk model.