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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]
EN
The article discussesd the impact of chosen behavioural factors on the imprecision of present value assessment. The formal model of behavioural present value is offered as a result of this discussion. The behavioural present value is described here as an intuitionistic fuzzy set. The significance of the replacement of a fuzzy set by an intuitionistic fuzzy set is proved.
EN
The main aim of this article is to present an uncomplicated method of estimating return rate on a portfolio of securities with Present Values presented as triangular fuzzy numbers. Determined return rates on the securities are not triangular fuzzy numbers. Despite this, we achieved a solution that is based on the arithmetic of triangular fuzzy numbers. The whole considerations are illustrated by a numerical example.
PL
Głównym celem artykułu jest przedstawienie nieskomplikowanej metody szacowania stopy zwrotu z portfela instrumentów finansowych o wartościach bieżących przedstawionych jako trójkątne liczby rozmyte. Wyznaczone stopy zwrotu z poszczególnych składników nie są trójkątnymi liczbami rozmytymi. Pomimo tego uzyskano takie rozwiązanie, które bazuje na arytmetyce trójkątnych liczb rozmytych. Całość rozważań zilustrowano przykładem numerycznym.
EN
The return rate is considered here as a fuzzy probabilistic set. Then the expected return is obtained as a fuzzy subset in the real line. This result is a theoretical foundation for new investment strategies. All considered strategies result of comparison profit fuzzy index and limit value. In this way we obtain an imprecise investment recommendation. Financial equilibrium criteria are a special case of comparison of the profit index and the limit value. The following criteria are generalized here: the Sharpe's Ratio, the Jensen's Alpha and the Treynor's Ratio. Moreover, the safety-first criteria are generalized here for the fuzzy case. The Roy Criterion, the Kataoka Criterion and the Telser Criterion are also generalized. Obtained results show that proposed theory is useful for the investment applications.
PL
Wartość bieżąca jest rozważana jako użyteczność strumienia finansowego. Dzięki temu można było określić, w jaki sposób awersja do ryzyka utraty płynności wpływa na stopę dyskonta. Otrzymany model został zastosowany w finansach behawioralnych.
EN
Present value is considered as the utility of cash flow. Therefore discount rate is presented as a trend dependent on risk aversion. Obtained model was applied for behavioural finance.
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EN
Theoretical basis for discussion is the natural nonlinear preorder defined on the set of financial flows. Then there exists a utility function consistent with this preorder. Two financial flows are equivalent iff their utilities are equal. Then we can show that the present value of financial flow is equal to its utility. Lack of capital synergy is not a necessary condition for this thesis.
PL
Rozważana jest stopa zwrotu, zdefiniowana jako rosnąca funkcja wartości przyszłej i malejąca funkcja wartości bieżącej. Niepewna wartość przyszła opisana jest za pomocą zmiennej losowej. Nieprecyzyjna wartość bieżąca jest reprezentowana przez intuicyjny zbiór rozmyty. Wtedy, zgodnie z uogólnioną zasadą rozszerzenia Zadeha, stopa zwrotu jest wyznaczona jako intuicyjny rozmyty zbiór probabilistyczny. Wyznaczona jest intuicyjna rozmyta oczekiwana stopa zwrotu oraz czterowymiarowy obraz ryzyka obarczającego tę stopę. W Dodatku zaprezentowano narzędzia formalne stosowane do opisu ryzyka.
EN
The return rate is determined here by present value given as intuitionistic fuzzy subset and by anticipated future value given as a random variable. In this way using the Zadeh’s extension principle, we obtain return rate described by an intuitionistic fuzzy probabilistic set. For this case expected return rate is calculated as an intuitionistic fuzzy subset in the real line. Four-dimensional risk image is introduced. In the Appendix we discuss formal tools which are applied for describing risk.
EN
There are presented premises inducing to generalize the concept of cash flow equivalence to fuzzy case. As a result of taking these studies was obtained membership function of fuzzy relation of cash flow equivalence. Obtained model was applied for determine the length of accounting period used in conditions of high inflation.
EN
The behavioural present value is defined as a fuzzy number assessed under the impact of chosen behavioural factors. The first formal model turned out to be burdened with some formal defects which are finally corrected in the presented article. In this way a new modified formal model of a behavioural present value is obtained. New model of the behavioural present value is used to explain the phenomenon of market equilibrium on the efficient financial market remaining in the state of financial imbalance. These considerations are illustrated by means of extensive numerical case study.
EN
The main objective of this research was to determine the synoptic and thermodynamic conditions accompanying the development of two severe thunderstorms that caused significant damage in Warsaw. The storm events of 17 June and 4 September 2016 were analysed. Materials used in the research included meteorological, aerological and radar data, as well as the Fire Service interventions database. These data allowed the conditions for the formation of the storms and their spatial variations in terms of intensity to be determined. It was shown that damage in Warsaw was caused by phenomena associated with supercell storms that developed in a moderate CAPE environment and a strong shear. It was confirmed that the geometry of the city increased the wind speed and modified its direction locally. In addition, it was found that the data on the number of Fire Service interventions clearly reflected the spatial variations in storm intensity by corresponding radar signatures to the high intensity of meteorological phenomena.
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