A Fuzzy Random Portfolio Optimization by Possibility-based Model

Conventional portfolio optimization models have an assumption that the future condition of stock market can be accurately predicted by historical data. Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean–variance model, chance constrained programming model and so on. This paper discusses the fuzzy random portfolio optimization problem where the asset returns are represented by fuzzy random variables. Possibility-based model are utilized for the solution method of portfolio optimization problem with fuzzy random returns. two-level mathematical programs is formulated to calculate the upper bound and lower bound of the return of the portfolio optimization problem that the lower bound calculate by historical data and the upper bound calculate by new information of stock market received during the constant time. A numerical example illustrates the whole idea on fuzzy random portfolio optimization problem.