Dynamical Aspects in Fuzzy Decision Making pp 141-162 | Cite as

# Fuzzy Portfolio Model for Decision Making in Investment

## Abstract

Financial engineering is one of the most important fields, today. Soft-computing methodologies are widely employed in financial engineering. Many problems of decision-making in investment have mainly been studied from optimizing points of view. As the investment is much influenced by the disturbance of a social and economical circumstances, optimization approach is not always the best. It is because problems used to be ill-structured under such influences. Therefore, a satisfaction approach is much better than an optimization one. In this discussion, we employ the aspiration level on the base of past experiences and knowledge possessed by a decision maker to treat a problem. That is, the aspiration level of the decision maker should be considered to solve a problem from the perspective of satisfaction strategy. It is more natural that the vague aspiration level of a decision maker is denoted as a fuzzy number.

In this chapter, the new methodologies in dealing with portfolio selection are studied. We explain the fuzzy approach to the decision making in portfolio selection problems after illustrating Bellman-Zadeh’s decision-making approach under uncertain environments and the fuzzy mathematical programming formulated by H. -J. Zimmermann. Before explaining the detail of the method of fuzzy portfolio selections, we survey the various soft-computing approaches to decision-makings in financial egnineering.

First, the recent methodologies related to portfolio selection are explained, which including neural networks, genetic algorithm chaotic analysis and fuzzy approach. Then fuzzy programming method is discussed. The fuzzy portfolio method is formulated and illustrated using an example.^{1}

## Keywords

Membership Function Fuzzy Number Portfolio Selection Aspiration Level Fuzzy Goal## Preview

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