Issue: 2011/Vol.21/No.2, Pages 65-78
EFFECTIVENESS OF SECURITIES WITH FUZZY PROBABILISTIC RETURN
Krzysztof M. Piasecki
Cite as: K. M. Piasecki. Effectiveness of securities with fuzzy probabilistic return. Operations Research and Decisions 2011: 21(2), 65-78.
Abstract
The generalized fuzzy present value of a security is defined here as fuzzy valued utility of cash flow. The generalized fuzzy present value cannot depend on the value of future cash flow. There ex- ists such a generalized fuzzy present value which is not a fuzzy present value in the sense given by some authors. If the present value is a fuzzy number and the future value is a random one, then the re- turn rate is given as a probabilistic fuzzy subset on a real line. This kind of return rate is called a fuzzy probabilistic return. The main goal of this paper is to derive the family of effective securities with fuzzy probabilistic return. Achieving this goal requires the study of the basic parameters characteriz- ing fuzzy probabilistic return. Therefore, fuzzy expected value and variance are determined for this case of return. These results are a starting point for constructing a three-dimensional image. The set of effective securities is introduced as the Pareto optimal set determined by the maximization of the ex- pected return rate and minimization of the variance. Finally, the set of effective securities is distin- guished as a fuzzy set. These results are obtained without the assumption that the distribution of fu- ture values is Gaussian.
Keywords: behavioural present value, fuzzy present value, random future value, fuzzy probabilistic return, effective financial security
Received: Accepted: