Effectiveness of Securities with Fuzzy Probabilistic Return
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 som...
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| Format: | Article |
| Language: | English |
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Wrocław University of Science and Technology
2011-01-01
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| Series: | Operations Research and Decisions |
| Online Access: | http://orduser.pwr.wroc.pl/DownloadFile.aspx?aid=183 |
| _version_ | 1818510287577284608 |
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| author | Krzysztof Piasecki |
| author_facet | Krzysztof Piasecki |
| author_sort | Krzysztof Piasecki |
| collection | DOAJ |
| description | 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. (original abstract) |
| first_indexed | 2024-12-10T22:57:11Z |
| format | Article |
| id | doaj.art-0aec1ae5f96c4e33903b15accb32e07b |
| institution | Directory Open Access Journal |
| issn | 2081-8858 2391-6060 |
| language | English |
| last_indexed | 2024-12-10T22:57:11Z |
| publishDate | 2011-01-01 |
| publisher | Wrocław University of Science and Technology |
| record_format | Article |
| series | Operations Research and Decisions |
| spelling | doaj.art-0aec1ae5f96c4e33903b15accb32e07b2022-12-22T01:30:14ZengWrocław University of Science and TechnologyOperations Research and Decisions2081-88582391-60602011-01-01vol. 21no. 26578171210713Effectiveness of Securities with Fuzzy Probabilistic ReturnKrzysztof Piasecki0Poznań University of Economics, PolandThe 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. (original abstract)http://orduser.pwr.wroc.pl/DownloadFile.aspx?aid=183 |
| spellingShingle | Krzysztof Piasecki Effectiveness of Securities with Fuzzy Probabilistic Return Operations Research and Decisions |
| title | Effectiveness of Securities with Fuzzy Probabilistic Return |
| title_full | Effectiveness of Securities with Fuzzy Probabilistic Return |
| title_fullStr | Effectiveness of Securities with Fuzzy Probabilistic Return |
| title_full_unstemmed | Effectiveness of Securities with Fuzzy Probabilistic Return |
| title_short | Effectiveness of Securities with Fuzzy Probabilistic Return |
| title_sort | effectiveness of securities with fuzzy probabilistic return |
| url | http://orduser.pwr.wroc.pl/DownloadFile.aspx?aid=183 |
| work_keys_str_mv | AT krzysztofpiasecki effectivenessofsecuritieswithfuzzyprobabilisticreturn |