تبيين و آزمون الگوريتم روش تسلط تصادفي براي ارزيابي كارايي پرتفوي بهينه

Investigation and Test Algorithm of Stochastic Dominance for Evaluation of Optimum Portfolio Efficiency.

Concepts similar to stochastic dominance have been known for many years but the two papers published by Hadar and Russell, and Hanoch and Levy in 1969, and the paper published by Rochschild and Stiglitz in 1970 paved the way for a new paradigm called stochastic dominance, with hundreds of studies following in their tracks. These studies, deal with theoretical as well as empirical issues in various areas of economics, finance, accounting, statistics, agriculture, and medicine. The need to develop the stochastic dominance rules stems from paradoxes that are sometimes revealed by the commonly used mean-variance rule. To be more specific, there are cases in which a clear-cut choice between two risky assets exists, yet the mean-variance rule is unable to rank the two alternate investments. Let us assume we have two alternative investments: x providing $1 or $2 with equal probability and y providing $2 or $4 with equal probability. A simple calculation shows that both the mean and the variance of y are greater than the corresponding parameters of x; hence the mean-variance rule remains silent regarding the choice between x and y. Yet, any rational investor would (and should) select y, because the lowest return on y is equal to the largest return on x. Well, this is a trivial case in which the mean-variance rule fails to show the superiority of one investment over another. However, there are many more such cases in which the mean-variance rule is unable to rank two investments.