GA Method For Programs With Second Order Stochastic Dominance Constraints

Stochasitc dominance is a fundamental concept in decision theory and economics, and it has played an important role in understanding and solving the issue of negotiable securities. The notion of stochastic dominance as a constraint was introduced for optimizaition problems, which as a new model of risk aversion is widely concerned by domestic and foreign scholars. This concept has been playing an important role in portfolio optimization. However, due to the semi-infinite and non smooth of constraints, it is difficult to solve by existing algorithms. In this paper, we introduce t genetic algorithm to solve the problem of second order stochastic dominance. The algorithm, as a kind of intelligent algorithm, does not need to require the subdifferentiability and meet the Slater constraint qualification of the constraint model. The introduction of the algorithm enriches the method of solving the stochastic dominance problem, and improves the efficiency and accuracy of the stochastic dominance model. Finally, the numerical results of the portfolio optimization problem prove that the algorithm has the advantage of solving the problem of stochastic dominance.