The Research On Portfolio Optimization Models With Second Order Stochastic Dominant Constraints And Numerical Methods

Stochastic dominance is a fundamental concept in economics and decision theory. In the ?nancial market of uncertainty, because the portfolio model with stochastic dominance constraints can avoid high-risk investments and it meet the risk preference of the investor, it is very important for theory and practical to research the portfolio optimization models of stochastic dominant.In this paper, we consider the portfolio optimization problems with second order stochastic dominant constraints, the main works include the following two aspects:Firstly, for a period of portfolio problem, we discuss the one-stage portfolio optimization models of stochastic dominant. At the beginning we introduced a transaction costs function and established the optimization models of second order stochastic dominant with transaction costs in order to research the portfolio optimization problem. We provide a smoothing approximation penalty function method for solving the problem. We use the sample average approximate method to the expected values of the underlying random functions and then reformulate the discrete model as an ordinary nonlinear programming model with?nite number of constraints. Then we design a exact penalty function to deal with limited constraint conditions and use a smoothing technique processing the non-smoothing function and penalty function. Numerical results prove that the model is e?cient and through comparing the smoothing approximation penalty function method and the traditional linear programming method, we found that the smoothing approximation penalty function method could substantially enhance eciency of compute and can solve the portfolio optimization problem eciently.Secondly, for two period of portfolio problem, we establish the two-stage portfolio optimization models with second order stochastic dominant and introduced a transaction costs function in the models. We provide a smoothing method and Linear programming algorithm for solving the two-stage stochastic minimization with second order stochastic dominant constraints. We use the sample average to approximate the expected values of the underlying random functions and then reformulate the discrete model as an ordinary two-stage programming problem with ?nite number of constraints. Then the problem of two-stage transformed into a single phase problem. Then we provide a smoothing method to solve the problem and compare with the traditional linear programming algorithm. Numerical results prove that the eectiveness and rationality of the new models and transaction costs can lead to change the investment strategy for investors and the smoothing method is better than the LP method and the second order random dominant constraint can eectively avoid high-risk invest.