Portfolio Model of Risk Management with Second Order Stochastic Dominant Constraints and Transaction Costs

In this paper, we introduced a transaction costs function and established a portfolio model of risk management with second stochastic dominance constraints. This model does not need to make any assumptions about the utility function of the investors and the distribution of the risk assets income, and it can ensure that the choices of the risk-averse investor can be randomly better than a reference value, so it can avoid the high risk investment. We provide a smoothing penalty sample average approximation method for solving this optimization problem. We prove that the smoothing penalty problem is equivalent to the original problem. Numerical results prove that the model and the method are efficient.