Fuzzy Portfolio Selection Models: A Numerical Study

In this chapter we analyze the numerical performance of some possibilistic models for selecting portfolios in the framework of risk-return trade-off. Portfolio optimization deals with the problem of how to allocate wealth among several assets, taking into account the uncertainty involved in the behavior of the financial markets. Different approaches for quantifying the uncertainty of the future return on the investment are considered: either assuming that the return on every individual asset is modeled as a fuzzy number or directly measuring the uncertainty associated with the return on a given portfolio. Conflicting goals representing the uncertain return on and risk of a fuzzy portfolio are analyzed by means of possibilistic moments: interval-valued mean, downside-risk, and coefficient of skewness. Thus, several nonlinear multi-objective optimization problems for determining the efficient frontier could appear. In order to incorporate possible trading requirements and investor’s wishes, some constraints are added to the optimization problems, and the effects of their fulfillment on the corresponding efficient frontiers are analyzed using a data set from the Spanish stock market.

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