Black-Litterman model with intuitionistic fuzzy posterior return

The main objective is to present a some variant of the Black - Litterman model. We consider the canonical case when priori return is determined by means such excess return from the CAPM market portfolio which is derived using reverse optimization method. Then the a priori return is at risk quantified uncertainty. On the side, intensive discussion shows that the experts' views are under knightian uncertainty. For this reason, we propose such variant of the Black - Litterman model in which the experts' views are described as intuitionistic fuzzy number. The existence of posterior return is proved for this case.We show that then posterior return is an intuitionistic fuzzy probabilistic set.Comment: SSRN Electronic Journal 201

Rozmyte zbiory probabilistyczne jako narzędzie finansów behawioralnych

The book is divided into five parts. The essence of behavioural finance is presented in the first parts. Fuzzy generalizations of some mathematical concepts are presented in the second part. The impact of selected behavioural premises for imprecise estimation of expected return is described in the third part. In the fourth part are considered financial instruments under uncertainty and imprecision risk. In the fifth part fuzzy probabilistic sets are applied for actuarial mathematics

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 Ward [35] or by Huang [14]. If the present value is a fuzzy number and the future value is a random variable, then the return rate is given as a probabilistic fuzzy subset on the 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

Behavioural Present Value: New Approach

W pracy Piaseckiego [Piasecki, 2011a; Piasecki, 2011b] zdefiniowano bieżącą wartość behawioralną jako liczbę rozmytą. Zaproponowany model formalny okazał się obarczony pewnymi usterkami formalnymi, które wypaczają obraz wpływu czynników behawioralnych. Usterki te przedstawiono w artykule. Następnie każdą z nich poprawiono. W ten sposób uzyskano nowy, zmodyfikowany model formalny behawioralnej wartości bieżącej. Model ten zastosowano do wyjaśnienia fenomenu utrzymywania się równowagi rynkowej na efektywnym rynku finansowym w stanie nierównowagi finansowej.Piasecki [in Piasecki, 2011a; Piasecki, 2011b] defined behavioural present value as a fuzzy number. The proposed model proved to be burdened with some formal defects which distorted the picture of the impact of behavioural factors. These defects are discussed in this paper. Next each of them is corrected. In this way, a modified formal model of behavioural present value is obtained. The new model is used to explain how market equilibrium is maintained in efficient financial markets remaining in the state in financial [email protected]. dr hab. Krzysztof Piasecki – Katedra Badań Operacyjnych, Uniwersytet Ekonomiczny w Poznani

Rozmyte zbiory probabilistyczne jako narzędzie finansów behawioralnych

The book is divided into five parts. The essence of behavioural finance is presented in the first parts. Fuzzy generalizations of some mathematical concepts are presented in the second part. The impact of selected behavioural premises for imprecise estimation of expected return is described in the third part. In the fourth part are considered financial instruments under uncertainty and imprecision risk. In the fifth part fuzzy probabilistic sets are applied for actuarial mathematics