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IMPRECISE RETURN RATES ON THE WARSAW STOCK EXCHANGE

100%
Piasecki K.
Metody Ilościowe w Badaniach Ekonomicznych
|
2014
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vol. 15
|
issue 1
153-158
EN
The return rate in imprecision risk may be described as a fuzzy probabilistic set [Piasecki, 2011a]. On the other side, in [Piasecki, Tomasik 2013] is shown that the Normal Inverse Gaussiandistribution is the best matching probability distribution of logarithmic returns on Warsaw Stock Exchange. There will be presented the basic properties if imprecise return with the Normal Inverse Gaussian distribution of future value logarithm. The existence of distribution of expected return rate is discussed. All obtained results may be immediately applied for effectiveness analysis at risk of uncertainty and imprecision [Pi-asecki, 2011c]
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Effectiveness of securities with fuzzy probabilistic return

88%
PIASECKI K. M.
Operations Research and Decisions
|
2011
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vol. 21
|
issue 2
65-78
EN
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 exists 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 return 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 characterizing 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 expected return rate and minimization of the variance. Finally, the set of effective securities is distinguished as a fuzzy set. These results are obtained without the assumption that the distribution of future values is Gaussian.
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