多目标条件风险值的一种近似求解方法

本文研究了一种求解多目标条件风险值问题的近似方法,首先引入了多个损失函数在对应的置信水平下关于一个证券组合的α-VaR损失值,以及α-CVaR损失值概念．α-CVaR损失值表明了在给定的证券组合于置信水平对应的最小信用风险值的条件期望损失值,那么求出这样的最小条件期望损失值的模型构成了一个求解α-CVaR损失值的多目标问题,它的解就是最小条件期望损失值的有效证券组合,即Pareto弱有效解．为了求解它的Pareto弱有效解,我们引进了损失函数对应的优化问题(SCVaR),可以通过求解非线性规划问题(SCVaR)的最优解近似地刻画α—CVaR损失值,这样使得求解α-CVaR损失值变得容易．

An Approximate Method on Solving Multiobjective Conditional Value-at-Risk

This paper study to solve an approximate method of multiobjective Conditional Value-at-Risk. We introduce the definitions of α-VaR loss value and α-CVaR loss value of multi loss function with respect to a portfolio under corresponding confidence level. The α-CVaR loss value indicate the conditional expectation loss value of α-VaR loss value with respect to a portfolio under corresponding confidence level. The model of solving α-CVaR loss value constitutes a multiobjective problem. The solution of the problem is the efficient portfolio, i.e. weak-Pareto efficient solution. In order to get weak-Pareto efficient solution under α-CVaR loss value, we define another optimal problem (SCVaR)of loss function. The α-CVaR loss value of MCVaR can approximately be described with the optimal solution of SCVaR, making it easy to solve.