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EN
Oriented fuzzy numbers are useful in portfolio management since they convey information regarding uncertainty and imprecision when considering financial markets. One may apply a fuzzy discount factor and an imprecise present value in the form of a trapezoidal oriented fuzzy number. An investor can obtain recommendations on individual stocks (buy, sell, accumulate, reduce). Analogous recommendations are also issued by experts. In such cases, recommendations are mostly based on available data and expert’s knowledge and experience. The purpose of the paper is to present a procedure for comparing the accuracy of both types of recommendations. Also, the real impact the recommendations have on potential changes in portfolio composition in trading-related industries is considered. The research uses quotations from companies from the trading sector of the Warsaw Stock Exchange (WSE). Theoretical considerations are presented in the form of an empirical case study.
EN
The article includes an analysis of a multiple asset portfolio, paying special attention to an imprecision risk, burdening the component instruments. The imprecision of decision premises is modeled in the imprecisely stated present value of portfolio assets, given subjectively by the investor in the form of trapezoidal fuzzy numbers. Next, for each asset and consisting portfolio we define imprecision measures appointed based on a fuzzy discounting factor. Analyzed theoretical model takes into account not only rational premises of a decision, but also allows for an inclusion of behavioral, technical and technological factors. During the performed research, relations between imprecision risk measures of assets and portfolio were found. Imprecision risk assessments are computed based on energy and entropy measures. Also, a case study is given, presenting mechanics of the model and methods of calculating risk measures. Performed analysis led to formulating some conclusions about the form and behavior of imprecision risk burdening a portfolio.
PL
Praca zawiera analizę portfela wieloskładnikowego pod kątem ryzyka nieprecyzyjności. Nieprecyzyjność przesłanek decyzyjnych jest modelowana nieprecyzyjnym określeniem wartości bieżącej instrumentów składowych portfela podanej subiektywnie przez inwestora w postaci trapezoidalnej liczby rozmytej. Dla poszczególnych składników oraz skonstruowanego z nich portfela określone są miary obarczającej je nieprecyzyjności, badanej na podstawie rozmytych czynników dyskontujących. Analizowany model teoretyczny, oprócz przesłanek racjonalnych, uwzględnia czynniki behawioralne oraz techniczne i technologiczne wpływające na decydenta. Oceny ryzyka nieprecyzyjności rozważanego portfela dokonano przy pomocy miar energii i entropii. Przedstawiono również studium przypadku prezentujące sposób działania modelu i metody obliczania miar nieprecyzyjności. Na podstawie przeprowadzonych badań sformułowano wnioski dotyczące postaci i zachowania ryzyka nieprecyzyjności portfela.
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