Two-level Linear Programming for Fuzzy Random Portfolio Optimization through Possibility and Necessity-based Model

In this paper, we deal with a portfolio optimization model involving fuzzy random variabels. Portfolio optimization is an important research field in modern finance. We consider the problem to maximize the the degree of both possibility and necessity that the objective function values satisfy the fuzzy goals. Using the possibility and necessity-based model, we reformulate the problem as a linear programming problem. In order to find the optimum solution, we propose two-level linear programming model to calculate the upper bound and lower bound of the objective function value separately. The lower bound calculates by historical data and the upper bound calculates by new information of stock market which is received during the constant time. Finally, we provide a numerical example to illustrate the proposed model.