信用风险优化中的期望短缺模型及基于非数值算法求解

期望短缺是一种新的风险量度和优化工具,它能够反映损失分布的尾部信息,从而有利于防范小概率极端金融风险;它能同时调整组合中所有头寸以优化期望短缺,同时得到相应受险价值.Fredrik给出了能同时优化组合期望短缺和受险价值的线性规划模型,但该模型存在维数障碍.为了克服这一障碍,本文将其重新变为一个非线性规划模型,并利用带约束的遗传算法和模拟退火算法求其近似最优解.实证研究表明:这两种方法都能够在很少改变期望收益的情况下,同时减少标准差、受险价值、期望短缺等重要风险衡量指标,但模拟退火算法对期望短缺指标优化效果更佳.

Expected Shortfall Modeling in Optimizing Credit Risk Portfolioand Its Solution Based on the Non-Numerical Algorithms

Expected Shortfall (ES) is a new tool for credit risk measure and optimization. As the risk measure tool, ES represents the tail information of loss and is favorable to keep away the extreme finance risk with very little probability. As the tool for risk optimization, it simultaneously adjusts all positions in the portfolio in order to optimize ES, and simultaneously gain corresponding VaR. Fredrik builds a linear program model with Expected Shortfall which can simultaneously optimize Expected Shortfall and VaR of portfolio, but this model has the drawback of dimension obstacle. To overcome this drawback, we revert it to a non-linear program model again and solve it by a Genetic Algorithm with constraints and Simulated Annealing Algorithm. Example illustration shows that the optimized portfolios' standard deviation, VaR and Exepected Shortfall are decreased obviously under the nearly same expected yield through two methods, but Simulated Annealing Algorithm has better effect on optimizing portfolio's ES.