The Present Value of a Portfolio of Assets With Present Values Determined by Trapezoidal Ordered Fuzzy Numbers

• Autorzy: Anna Łyczkowska-Hanćkowiak , Krzysztof Piasecki
• Języki publikacji: EN

Abstrakty

EN

We consider the obvious thesis that the present value of a portfolio is equal to the sum of the present values of its components. The main goal of this paper is the implementation of this thesis in the case when present values are determined by trapezoidal ordered fuzzy numbers. We apply the revised sum of ordered fuzzy numbers. The associativity of such a revised sum is investigated here. In addition, we show that the multiple revised sum of a finite sequence of trapezoidal ordered fuzzy numbers depends on the ordering of its summands. Without any obstacles, the results obtained can be generalized to the case of any ordered fuzzy numbers. (original abstract)

Słowa kluczowe

EN

Investment portfolio; Asset value; Cash flows; Case study

PL

Portfel inwestycyjny; Wartość aktywów; Przepływy pieniężne; Studium przypadku

• Czasopismo: Operations Research and Decisions
• Rocznik: 2018
• Tom: 28
• Numer: nr 2
• Strony: 41--56

Twórcy

autor

Anna Łyczkowska-Hanćkowiak

• WSB University in Poznań, Poland

autor

Krzysztof Piasecki

• Poznań University of Economics, Poland

Bibliografia

• [1] BUCKLEY I.J., The fuzzy mathematics of finance, Fuzzy Sets Syst., 1987, 21, 257-273.
• [2] DUBOIS D., PRADE H., Operations on fuzzy numbers, Int. J. System Science, 1978, 9, 613-629.
• [3] DUBOIS D., PRADE H., Fuzzy real algebra: some results, Fuzzy Sets Syst., 1979, 2, 327-348.
• [4] GUTIERREZ I., Fuzzy numbers and net present value, Scandinavian J. Manage., 1989, 5 (2), 149-159.
• [5] KOSHY T., Catalan Numbers with Applications, Oxford University Press, London 2008.
• [6] KOSIŃSKI W., PROKOPOWICZ P., ŚLĘZAK D., Drawback of fuzzy arithmetic - new intuitions and propositions, [In:] T. Burczyński, W. Cholewa, M. Moczulski (Eds.), Methods of Artificial Intelligence, PACM, Gliwice 2002, 231-237.
• [7] KOSIŃSKI W., PROKOPOWICZ P., ŚLĘZAK D., Fuzzy numbers with algebraic operations. Algorithmic approach, [In:] M. Klopotek, S.T. Wierzchoń, M. Michalewicz (Eds.), Proc. Intelligent Information Systems 2002, Sopot, Poland, Physica Verlag, Heidelberg 2002, 311-320.
• [8] KOSIŃSKI W., PROKOPOWICZ P., ŚLĘZAK D., Ordered fuzzy numbers, Bull. Pol. Acad. Sci., 2003, 51 (3), 327-338.
• [9] KOSIŃSKI W., On fuzzy number calculus, Int. J. Appl. Math. Comp. Sci., 2006, 16 (1), 51-57.
• [10] KUCHTA D., Fuzzy capital budgeting, Fuzzy Sets Syst., 2000, 111, 367-385.
• [11] LESAGE C., Discounted cash-flows analysis. An interactive fuzzy arithmetic approach, Eur. J. Econ. Soc. Syst., 2001, 15 (2), 49-68.
• [12] ŁYCZKOWSKA-HANĆKOWIAK A., Behavioural present value determined by ordered fuzzy number, SSRN Electr. J., 2017, DOI: 10.2139/ssrn.2988243.
• [13] ŁYCZKOWSKA-HANĆKOWIAK A., Behavioural present value in the form of ordered fuzzy numbers, Optimum: Studia Ekon., 2017, 87 (3), 122-137 (in Polish).
• [14] ŁYCZKOWSKA-HANĆKOWIAK A., PIASECKI K., On some difficulties in the addition of trapezoidal ordered fuzzy numbers, arXiv:1710.03541, 2017.
• [15] ŁYCZKOWSKA-HANĆKOWIAK A., PIASECKI K., The expected discount factor determined for present value given as ordered fuzzy number, [In:] W. Szkutnik, A. Sączewska-Piotrowska, M. Hadaś-Dyduch, J. Acedański (Eds.), Proc. 9th International Scientific Conference Analysis of International Relations 2018. Methods and Models of Regional Development. Winter Edition, University of Economics in Katowice Publishing, 2018, 69-75.
• [16] ŁYCZKOWSKA-HANĆKOWIAK A., PIASECKI K., On representation of Japanese candlesticks by ordered fuzzy numbers, [In:] W. Szkutnik, A. Sączewska-Piotrowska, M. Hadaś-Dyduch, J. Acedański (Eds.), Proc. 9th International Scientific Conference Analysis of International Relations 2018. Methods and Models of Regional Development. Winter Edition, University of Economics in Katowice Publishing, 2018, 61-68.
• [17] NISON S., Japanese Candlestick Charting Techniques, New York Institute of Finance, New York 1991.
• [18] PIASECKI K., Behavioural present value, SSRN Electr. J., 2011, DOI:10.2139/ssrn.1729351.
• [19] PIASECKI K., Basis of financial arithmetic from the viewpoint of the utility theory, Oper. Res. Dec., 2012, 22 (3), 37-53.
• [20] PIASECKI K., Expected return rate determined as oriented fuzzy number, [In:] P. Pražak (Ed.), Proc. 35th International Conference Mathematical Methods in Economics, Gaudeamus, University of Hradec Králové, 2017, 561-565.
• [21] PIASECKI K., On some modifications of ordered fuzzy numbers, Optimum: Studia Ekon., 2017, 87 (3), 3-18 (in Polish).
• [22] PIASECKI K., ŁYCZKOWSKA-HANĆKOWIAK A., Oriented behavioural present value of two-asset portfolio. A case study, Studia Ekonomiczne. Zeszyty Naukowe Uniwersytetu Ekonomicznego w Katowicach, 2018 (accepted for publication), (in Polish).
• [23] PIASECKI K., SIWEK J., Behavioural present value defined as fuzzy number. A new approach, Folia Oecon. Stetin., 2015, 15 (2), 27-41.
• [24] PIASECKI K., SIWEK J., Two-assets portfolio with trapezoidal fuzzy present values, [In:] W. Szkutnik, A. Sączewska-Piotrowska, M. Hadaś-Dyduch, J. Acedański (Eds.) Proc. 9th International Scientific Conference Analysis of International Relations 2018. Methods and Models of Regional Development. Winter Edition, Wydawnictwo Uniwersytetu Ekonomicznego w Katowicach, Katowice 2018, 76-82.
• [25] SHEEN J.N., Fuzzy financial profitability analyses of demand side management alternatives from participant perspective, Inf. Sci., 2005, 169, 329-364.
• [26] TSAO C.-T., Assessing the probabilistic fuzzy net present value for a capital investment choice using fuzzy arithmetic, J. Chinese Institute of Industrial Engineers, 2005, 22 (2), 106-118.
• [27] WARD T.L., Discounted fuzzy cash flow analysis, Proc. Fall Industrial Engineering Conference, University of California, Berkeley 1985, 476-481.
• [28] ZADEH L.A., The concept of a linguistic variable and its application to approximate reasoning. Part I. Information linguistic variable, Expert Syst. Appl., 1975, 36 (2), 3483-3488.
• [29] ZADEH L.A., The concept of a linguistic variable and its application to approximate reasoning. Part II, Inf. Sci., 1975, 8 (4), 301-357.
• [30] ZADEH L.A., The concept of a linguistic variable and its application to approximate reasoning. Part III, Inf. Sci., 1975, 9 (1), 43-80.
• [31] https://www.bankier.pl/inwestowanie/profile/quote.html?symbol=WIG20 (accessed on: 22.01.2018).

Identyfikatory

DOI

10.5277/ord180203