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2011 | 21 | 2 | 65-78
Article title

Effectiveness of securities with fuzzy probabilistic return

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EN
Abstracts
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.
Year
Volume
21
Issue
2
Pages
65-78
Physical description
Contributors
  • Department of Operations Research, Poznań University of Economics, Poznań, Poland
References
  • BUCKLEY J.J., Fuzzy mathematics of finance, Fuzzy Sets and Systems, 1987, 21, 257–273.
  • BUCKLEY J.J., Solving fuzzy equations in economics and finance, Fuzzy Sets and Systems, 48, 1992, 289–296
  • CAMPOS L.M., GONZALES A., A subjective approach for ranking fuzzy numbers, Fuzzy Sets and Systems, 1989, 29, 145–153.
  • CHIU C.Y., PARK C.S. , Fuzzy cash analysis using present worth criterion, Eng. Econom., 1994, 39 (2), 113–138.
  • CZOGAŁA E., GOTTWALD S., PEDRYCZ W., Contribution to application of energy measure of fuzzy sets, Fuzzy Sets and Systems, 1982, 8, 205–214.
  • DACEY R., ZIELONKA P., A detailed prospect theory explanation of the disposition effect, Journal of Behavioral Finance, 2008, 9 (1), 43–50.
  • DOYLE, J.R., Survey of time preference, delay discounting models, Working Paper, Cardiff Business School, Cardiff University, 2010 [online], http://ssrn.com/abstract=1685861.
  • ECHAUST K., TOMASIK E., Wybrane rozkłady prawdopodobieństwa w modelowaniu empirycznych stóp zwrotu akcji notowanych na GPW w Warszawie, Zeszyt Naukowy Akademii Ekonomicznej w Poznaniu, 2008, 104, 34–66.
  • FREDERICK S., LOEWENSTEIN G., O’DONOGHUE T., Time Discounting and Time Preference: A critical Review, Journal of Economic Literature, 2002, 40, 351–401.
  • GOTTWALD S., CZOGAŁA E., PEDRYCZ W., Measures of fuzziness and operations with fuzzy sets, Stochastica, 1982, 6, 187–205.
  • GREENHUT J.G., NORMAN G., TEMPONI C., Towards a fuzzy theory of oligopolistic competition, IEEE Proceedings of ISUMA-NAFIPS 1995, 1995, 286–291.
  • GUTIERREZ I., Fuzzy numbers and net present value, Scand. J. Mgmt., 1989, 5 (2), 149–159.
  • HIROTO K., Concepts of probabilistic sets, Fuzzy Sets and Systems, 1981, 5, 31–46.
  • HUANG X., Two new models for portfolio selection with stochastic returns taking fuzzy information, European Journal of Operational Research, 12007, 80 (1), 396–405.
  • KAHNEMAN D., TVERSKY A., Prospect theory: an analysis of decision under risk, Econometrica, 1979, 47, 263–292.
  • KAPLAN S., BARISH N.N., Decision-making allowing uncertainty of future investment opportunities, Management Science, 1967, 13 (10), 569–577.
  • KILLEEN P.R., An additive-utility model of delay discounting, Psychological Review, 2009, 116, 602–619.
  • KONTEK, K., Decision utility theory: Back to von Neumann, Morgenstern, and Markowitz, Working Paper, 2010 [online]: http://ssrn.com/abstract=1718424.
  • KUCHTA D., Fuzzy capital budgeting, Fuzzy Sets and Systems, 2000, 111, 367–385.
  • KWAKERNAAK H.K., Fuzzy random variables I, Information Sciences, 1978, 15, 1–29.
  • KWAKERNAAK H.K., Fuzzy random variables II, Information Sciences, 1979, 17, 253–278.
  • LESAGE C., Discounted cash-flows analysis. An interactive fuzzy arithmetic approach, European Journal of Economic and Social Systems, 2001, 15 (2), 49–68.
  • MARKOWITZ H.S.M., Portfolio selection, Journal of Finance, 1952, 7, 77–91.
  • MISES L. VON, The ultimate foundation of economic science. An essay on method, D. van Nostrand Company, Inc., Princeton, 1962.
  • PIASECKI K., Decyzje i wiarygodne prognozy, Zeszyty Naukowe, s. I. Prace doktorskie i habilitacyjne, z. 106, Akademia Ekonomiczna w Poznaniu, Poznań, 1990.
  • PIASECKI K., O sposobie poszukiwania dobrej metody inwestowania na giełdzie, [in]: J. Hozer (Ed.), Metody ilościowe w ekonomii, Uniwersytet Szczeciński, Studia i Prace Wydziału Nauk Ekonomicznych i Zarządzania nr 11, Szczecin, 2009, 387–398.
  • PIASECKI K., Behavioural present value, Behavioral and Experimental Finance eJournal, 2011 (4), [online].
  • PIASECKI K., ZIOMEK R., Zbiory intuicyjne w prognozowaniu rynku finansowego, Zeszyty Naukowe Uniwersytetu Szczecińskiego, Finanse, Rynki Finansowe, Ubezpieczenia, 2010, 28, 45–60.
  • SHEEN J.N., Fuzzy financial profitability analyses of demand side management alternatives from participant perspective, Information Sciences, 2005, 169, 329–364.
  • TOMASIK E., Rozkłady prawdopodobieństwa stop zwrotu indeksów i akcji notowanych na GPW w Warszawie, [in:] W. Ostasiewicz (Ed.), Statystka aktuarialna – teoria i praktyka, Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu, Wrocław, 2008, 24–38.
  • TOMASIK E., Homogeneity hypothesis for tail index of return rate distributions, [in:] P. Chrzan, T. Czernik (Eds.), Innowacje w finansach i ubezpieczeniach. Metody matematyczne, ekonometryczne i informatyczne, Wydawnictwo Akademii Ekonomicznej w Katowicach, Katowice, 2009, 147–159.
  • TOMASIK E., PIASECKI K., Return rates of WIG20 index in the situation of extreme tide turning on the Warsaw Stock Exchange, Capital Markets: Asset Pricing & Valuation eJournal, 2011, 4 (4), [online].
  • TOMASIK E., WINKLER-DREWS T., Rozkłady stabilny, uogólniony Pareto oraz t-Studenta w modelowaniu dziennych stóp zwrotu indeksu WIG20, [in:] P. Chrzan, T. Czernik (Eds.), Innowacje w finansach i ubezpieczeniach. Metody matematyczne, ekonometryczne i informatyczne, Wydawnictwo Akademii Ekonomicznej w Katowicach, Katowice, 2009, 101–110.
  • TSAO C.-T., Assessing the probabilistic fuzzy net present value for a capita. Investment choice using fuzzy arithmetic, J. Chin. Ins. Industrial Engineers, 2005, 22 (2), 106–118.
  • WARD T.L., Discounted fuzzy cash flow analysis, Proceedings of 1985 Fall Industrial Engineering Conference, Seattle, 1985, 476–481.
  • WINKLER-DREWS T., Zarządzanie ryzykiem zmiany ceny, PWE, Warszawa, 2009.
  • ZAUBERMAN G., KYU KIM B., MALKOC S., BETTMAN J.R., Discounting time and time discounting: Subjective time perception and intertemporal preferences, Journal of Marketing Research, 2009, 46, 543–556.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-db269f14-d0a7-4ccc-a3eb-7d7250ee4956
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