CVaR风险度量下的安全第一标准

Safety-first criteria under conditional value-at-risk

通过优化方法给出了在均值 CVaR有效前沿上,满足给定的三种安全第一标准的最优证券组合、最优证券组合的期望收益及其CVaR风险值的求解方法和相关结果.三种安全第一标准的经济意义分别如下使证券组合的回报率低于给定的生存水平的概率达到最小;在证券组合的回报率低于生存水平的概率不超过指定值的条件下,使它的生存水平达到最大;在证券组合的回报率低于给定生存水平的概率不超过指定值的条件下,使它的回报率的期望值达到最大.这些结果可为金融机构和投资者正确决策提供理论依据.

In this paper, we proposed a method and relevant results of determining the optimal portfolio, its corresponding expectation of return and its value of conditional value-at-risk satisfying the given safety criteria on the portfolio expectation return-conditional value-at-risk efficient frontier according to the three types of safety-first criteria. Three types of safety-first criteria implied that the probability of the portfolio returns less than some setting upper bound should reach the minimum, or the upper bound of the portfolio returns should get the maximum while the probability of the portfolio returns less than the upper bound is smaller than a given value, or the expectation of the portfolio returns should attain the maximum while the probability of the portfolio returns less than some setting upper bound is smaller than a given value, respectively. These results can provide theoretical basis for financial institutions and investors to make correct decisions.