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EN
The attractiveness of structured products is mainly due to the fact that the diversity of their structures corresponds to the specific preferences of different groups of investors. To determine the appropriate investment product for an investor it is necessary to identify investor preferences, attitude toward risk. The paper contains an analysis of investors preferences in relation to the payoffs from the typical structured products. Investors’ preferences are based both on the rational choice theory and the prospect theory.
EN
The work is a continuation of a series of works by A. Binderman- Dubik, published in the years 2004 - 2013, concerning the regional differentiation of Polish agriculture, in which she used two patterns (models): negative and positive. These studies showed the superiority of the two-pattern methods used over the single-pattern methods. Here, methods based on three patterns (negative, positive, indirect) are used. The author uses the method considered by the authors: Binderman Z., Borkowski B., Szczesny W. 2020.
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Taxing foreign capital in Brazil: a sequential game

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EN
Emerging market economies have witnessed a surge in capital inflows as a result of monetary expansion in developed countries in the aftermath of the 2008 crisis. In this paper, we have modeled the Brazilian decision to tax foreign capital inflows, which were deemed to hurt country’s firm’s competitiveness as they made the Real currency stronger. We have presented a game between three players in which each agent maximizes its utility function in a sequential framework. The main result is that with everything else held constant the Brazilian government’s decision to tax foreign capital leads to an increase in domestic interest rates. Cost of capital should raise as a consequence of the strategic behavior of involved actors, namely the government, domestic banks and foreign investors. A cautious approach on those measures is then warranted.
EN
Research background: In the distributive analysis, the constant relative inequality aversion utility function is a standard tool for ethical judgements of income distributions. The sole parameter ? of this function expresses a society?s aversion to inequality. However, the profession has not committed to the range of ?. When assessing inequality and other welfare characteristics, analysts assume an arbitrary level of ?, common to all countries and years. This assumption seems unjustified. Purpose of the article: This paper aims to estimate the parameter ? for each country and year individually using datasets from the Luxembourg Income Study Database in all available years, which dates back to the 1970s. Methods: We utilise the method of estimating ?, which assumes the generalised beta of the second kind distribution of incomes. The estimator of ? is derived from the mathematical condition of the existence of the social welfare function.  Findings & value added: We have elaborated an ?atlas? of  388 estimates of ? for 55 countries across time. Inequality aversion is country-year specific, with a minimum of 0.97 and a maximum of 3.8. Ninety per cent of all estimates are less than 2.5. Inequality aversion is negatively correlated with income inequality, but it is independent of economic development. Thus, inequality aversion appears as an additional dimension of the classical inequality-development relationship. This article contributes to solving a fundamental problem of Welfare Economics: directly measuring the social utility of income (welfare) function. The estimates of ? for 55 countries imply a complete knowledge of these countries' constant relative inequality aversion utility functions.
EN
The article presents a problem of proper hedging strategy in expected utility model when forward contracts and options strategies are available. We consider a case of hedging when an investor formulates his own expectation on future price of underlying asset. In this paper we propose the way to measure effectiveness of hedging strategy, based on optimal forward hedge ratio. All results are derived assuming a constant absolute risk aversion utility function and a Black-Scholes framework.
PL
Z wcześniejszych badań wynika, że istnieje kilka modeli podejmowania decyzji ekonomicznych w gospodarstwach domowych. Jednym z nich jest podejmowanie decyzji wspólnie przez członków gospodarstwa domowego. W artykule przedstawiono kilka różnych sposobów kompromisowych decyzji w przypadku, gdy dwoje członków gospodarstwa domowego ma różne funkcje użyteczności dwóch blisko substytucyjnych dóbr. Następnie sprawdzono, jak sposób rozumienia kompromisu wpływa na kształtowanie się popytu gospodarstwa domowego na te dobra.
EN
The previous research shows that there are a few models of the economic decision making in households. One of them is joint decision making by members of the household. In this paper a few different ways of compromise decisions are presented when two members of the household have different utility functions of two closely substitutable goods. Then we have examined how the way of understanding a compromise affects the demand for these goods in the household.
EN
This study outlines the decision-making process under risk considering the psychological aspects of the decision-maker. The aim is to construct a principle of an optimal decision for an individual decision-maker. The study considers a finite, d iscrete s et o f a cceptable decisions, a set of possible world states and a system of probabilities of these states (where the probabilities are either known or subjectively estimated by the decision-maker), and a utility matrix of making each decision in particular world states. The proposed process of optimizing the decision addresses not only the rationality of the person making but also emotional aspects of the person making the decision. Rationality is represented by the value of the utility function of the benefits r esulting f rom m aking a d ecision i n a p ossible w orld s tate. The behavioral part of the model involves two emotions important to decision-making: regret over making a decision that brought less utility than possible in the given conditions and satisfaction with the choice which proved better than the worst option. The first e motion is represented by the regret function and the other by the satisfaction function. New notions are defined: relative utility and expected relative utility of particular decisions used to construct the principle of an optimal decision under risk. The presented theory thus supplements the prospect theory, as it accounts for regret and satisfaction in the decision-making process under risk. This idea is part of behavioral economics, yet not standing in opposition to classical economics. Its advantage is that it considers both psychological and rational factors in the decision-making process.
EN
In this note we propose a calculus for piece-wise linear functions, in order to obtain derivatives and second derivatives at points where the function is not differentiable. Such derivatives can be used to calculate coefficients of risk aversion at initial wealth for piece-wise linear utility functions for gains, which display loss aversion-and hence non differentiability at zero gains.
EN
In the article an issue of choice about the optimum decision in conditions of the uncertainty identified here with multiple choice was discussed. They are being met among others in the portfolio analysis. With purpose which was put and they were trying to achieve taking the best decision in the financial or economic context by the person entertaining her was supposed to be. For solving this problem the concepts of the utility function, the random utility function and the weighed utility function were implemented. Also determined here changes of the external environment in the time as the influence of the environment were taken into account through different his states. These states are characteristic with homogeneous Markov chain. As the criterion for the choice of the decision a random utility function was exploited. She also constitutes the objective function of the optimization problem with constraints. Also a practical example for functioning of proposed methodology was expressed based on the specified set of utility functions.
PL
W artykule omówiono zagadnienie wyboru optymalnej decyzji w warunkach niepewności utożsamianej tu z wielokrotnym wyborem. Spotyka się je między innymi w analizie portfela. Celem, który postawiono i starano się osiągnąć miało być podjęcie lepszej decyzji w kontekście finansowym bądź ekonomicznym przez osobę ją podejmującą. Do rozwiązania tego problemu wprowadzono koncepcje funkcji użyteczności, losowej funkcji użyteczności oraz ważonej funkcji użyteczności. Uwzględniono też zmiany otoczenia zewnętrznego w czasie określane tu jako wpływ środowiska poprzez różne jego stany. Stany te charakteryzowane są jednorodnym łańcuchem Markowa. Jako kryterium wyboru decyzji wykorzystano losową funkcję użyteczności. Ona też stanowi funkcję celu do rozwiązania właściwego tu problemu optymalizacyjnego z ograniczeniami. Zaprezentowany został też przykład praktyczny dla funkcjonowania proponowanej metodyki w oparciu o zadane funkcje użyteczności.
EN
The work is a direct continuation of the series of authors articles concerning the construction of new indicators of classification. In the present paper, a manner of classification of objects which is based on three model objects is proposed. An example of the actual distribution of a bonus fund among business units in a large corporation demonstrates the usefulness of such an approach. Studies have shown that this method is very useful for organizing and grouping objects.
PL
W pracy zaproponowano użycie oprócz wzorców negatywnego i pozytywnego dodatkowego wzorca pośredniego do budowy miernika syntetycznego, przeznaczonego do porządkowania i podziału obiektów na grupy. Na przykładzie rzeczywistego podziału funduszu premiowego pomiędzy jednostki biznesowe w dużej korporacji, zaprezentowano użyteczność takiego podejścia. Przeprowadzone badania wykazały dużą przydatność omówionej metody do porządkowania i grupowania obiektów.
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