Random credibilitic portfolio selection problem with different convex transaction costs

Most of the portfolio optimization problems are devoted to either stochastic model or fuzzy one. However, practical portfolio selection problems often involve the mixture of the stochastic returns with fuzzy information. In this paper, we propose a new mean variance random credibilitic portfolio selection problem with different convex transaction costs, i.e., linear function, non-smooth convex function, smooth convex function. In this proposed model, we assume that the returns of assets obey the trapezoidal-type credibilitic distributions, and the risks obey the stochastic distributions. Based on the random credibilitic theories, these models are transformed into crisp convex programming problems. To find the optimal solution, we, respectively, present a pivoting algorithm, a branch-and-bound algorithm, and a sequence quadratic programming algorithm to solve these models. Furthermore, we offer numerical experiments of different forms of convex transaction costs to illustrate the effectiveness of the proposed model and approach.