均值-VaR模型的一种新解法：鞍点近似、遗传算法

以均值度量收益,方差度量风险的均值.方差模型,广泛应用于资产组合优化.随着对金融风险度量方法研究的不断深入,VaR作为一种简便、易于理解的风险度量方法,在金融企业中得到日益广泛的应用.本文用VaR代替均值-方差模型中的方差,构建了均值-VaR模型应用干投资组合优化.均值-VaR模型是非线性规划,仅当VaR满足凸性和可微性的前提下,满足库恩-塔克条件的解才是全局最优解.本文在CreditRisk+框架下,提出一个在不允许卖空条件下,不需对VaR的性质做出前提假定的新解法:将鞍点近似法用于计算VaR,在资产头寸与VaR之间建立起函数关系,采用遗传算法寻找模型的近似最优解.并用一个债券组合说明该方法的有效性。

A Numeric Approach to Solve Mean-VaR Model:Saddle-point Approximation and Genetic Algorithm

Mean-variance model has a wide application in optimizing asset portfolio.As the researches for risk measure tools are deeper,VaR as an convenient and easily understandable tool becomes more and more popular in financial organizations.In this paper we substitute VaR for variance in mean-variance model and build mean-VaR model to optimize the asset portfolio.Mean-VaR model is nonlinear program, and on the premise of convexity and differentiability of VaR,the solution meeting Kuhn-Tucker condition is the globally optimal for nonlinear program.This paper provides a new approach to solve it,and it does not need the premises for VaR.Compute VaR taking advantage of saddle-point approximation and make VaR to be the function of asset positions under the frame of CreditRisk+ and find the optimal solution for the model by genetic algorithm.At last,a portfolio of bonds as an example is used to illustrate the validity of the approach.