Analysis of Complex Decision Problems Based on Cumulative Prospect Theory

Complex risky decision problems involve sequences of decisions and random events. The choice at a given stage depends on the decisions taken in the previous stages, as well as on the realizations of the random events that occurred earlier. In the analysis of such situations, decision trees are used, and the criterion for choosing the optimal decision is to maximize the expected monetary value. Unfortunately, this approach often does not reflect the actual choices of individual decision makers. In descriptive decision theory, the criterion of maximizing the expected monetary value is replaced by a subjective valuation that takes into account the relative outcomes and their probabilities. This paper presents a proposal to use the principles of cumulative prospect theory to analyse complex decision problems. The concept of a certainty equivalent is used to make it possible to compare risky and non-risky alternatives. (original abstract

Evaluation of Stock Market Decisions Based on Cumulative Prospect Theory

Both the prospect theory as well as the cumulative prospect theory are aimed at explaining the way the decision-maker see and evaluate risky decisions. They allow for the explanation of some inconsistency between observed decision-makers behaviours and axioms of the expected utility theory. For years financial aspects of cumulative prospect theory are the subject of many research studies. The purpose of the paper is to review some issues connected with the cumulative prospect theory and its application to financial market. Presented papers concern issues related to the value functions, concept of loss aversion and the construction of portfolio selection models with some simplifying assumptions. In our paper we also present observed in real life, but often mysterious, behaviours of investors, who evaluate investment choices relative to some reference point, feel loss aversion and revalue objective probabilities

Valuation of Decision Alternatives with Continuous Distributions Based on Prospect Theory

Niewątpliwą wadą modelu teorii perspektywy jest możliwość oceny wariantów decyzyjnych złożonych z co najwyżej dwóch niezerowych wyników. Wada ta uniemożliwia stosowanie jej na większą skalę, gdyż w większości rzeczywistych wariantów decyzyjnych należy brać pod uwagę więcej możliwych wyników decyzji, a także często warianty decyzyjne mają ciągły rozkład prawdopodobieństwa. W pracy zostaną przedstawione koncepcje rozszerzające teorię perspektywy na warianty decyzyjne o rozkładach ciągłych oraz o rozkładach dyskretnych z więcej niż dwoma niezerowymi wynikami. Przykłady zastosowania prezentowanych modeli będą opierać się na rzeczywistych danych giełdowych.The work presents concepts extending prospect theory on decision-making alternatives with continuous distributions and discrete distributions with more than two non-zero outcomes. Examples of the application of the presented models will be based on real market data. The first part of the paper describes the principles of prospect theory, the second part shows the proposal of Rieger and Wang which extends the prospect theory to continuous distributions, also the extension to alternatives with more than two outcomes is presented. In the third section we give the example of the practical application of prospect theory for continuous distributions to create rankings of stocks belonging to the WIG20 index. We also built the rankings of these companies based on their valuation on the basis of prospect theory for discrete distributions

Wizualizacje w ocenie ryzyka inwestycyjnego i sterowaniu poziomem zapasów z wykorzystaniem programu GeoGebra

The development of information technology forces the usage of software tools in the analysis and visualisation of risk in various fields including economics, finance, management. The graphic presentation of analysis results as well as various relationships contributes to their better understanding. Modern computer software allows for showing dynamics of various decision problems. The aim of the paper is to present the dynamic visualisations of risk analysis in selected fields using the GeoGebra software.Rozwój technologii informatycznych wymusza korzystanie z programów komputerowych w zakresie analizy i wizualizacji ryzyka w różnych dziedzinach, w tym ekonomii, finansach, zarządzaniu. Graficzne przedstawienie wyników analizy, jak również różnych zależności, przyczynia się do ich lepszego zrozumienia. Nowoczesne oprogramowanie komputerowe pozwala na pokazywanie dynamiki różnych problemów decyzyjnych. Celem artykułu jest przedstawienie wybranych dynamicznych wizualizacji ryzyka utworzonych z wykorzystaniem programu GeoGebra

Omega Ratio in the Evaluation Of Decision Alternatives with a Continuous Probability Distribution on the Example of Shares Quoted on Warsaw Stock Exchange

W porównywaniu akcji notowanych na giełdzie stosuje się najczęściej kryteria wykorzystujące wybrane parametry rozkładu, wyznaczane na podstawie danych historycznych przy założeniu dyskretnego rozkładu losowych stóp zwrotu. Miarą uwzględniającą pełną informację o rozkładzie jest wskaźnik omega. W artykule przedstawiono przykład zastosowania wskaźnika omega do oceny akcji przy założeniu ciągłego rozkładu stóp zwrotu. Celem pracy jest empiryczna weryfikacja zależności uporządkowania (względem wskaźnika omega) losowych wariantów decyzyjnych od przyjętego rozkładu.When comparing shares quoted on the stock exchange, investors the most often use the criteria which are based on selected parameters of the probability distribution. In such approach historical date are being used and a discrete probability distribution of random returns is assumed. The omega ratio is a measure which takes into account all the information about the probability distribution. In this paper we present the example of applying the omega ratio to the evaluation of shares assuming a continuous distribution of returns. The aim of this paper is to empirically verify the relationship between the order (according to the omega ratio) of random decision alternatives and the assumed probability distribution

Application of Simulation Method in Valuation of Selected Stocks Based on Cumulative Prospect Theory

Cumulative prospect theory is the leading approach in a description of real choices. According to these rules decision-maker valuates distributions of possible relative outcomes of decision alternatives. An attempt to use these rules on stock market meets with some difficulties. On the one hand an investor has data concerning past quotations, and on the other hand he wants to know which stock to select now in order to obtain the best outcome in the future. The goal of this paper is to investigate whether the consideration of additional information about the distribution of future investment's outcomes can contribute to the selection of stocks which will yield higher real gains, than stocks selected on the basis of valuation of past outcomes

Almost Stochastic Dominance in Stocks Preselection

The stochastic dominance rules are a very popular tool in the support of decision making in various fields of economics and management. However the selection of the best alternative on the basis of stochastic dominance is sometimes impossible due to incomparability of alternatives. Some particular properties of almost second degree stochastic dominance (which stochastic dominance do not posses) allow to compare all elements of the set of random alternatives and to build a ranking of them. The aim of the article is to propose a stocks preselection method based on almost stochastic dominance. Our method allow to determine the set of the best stocks and thereby to reduce the number of stocks as a potential elements of a portfolio. Such reduction is very important nowadays because with every year more and more stocks are quoted on Stock Exchange in Warsaw

Comparison of the Valuations of Alternatives Based on Cumulative Prospect Theory and Almost Stochastic Dominance

There are commonly accepted and objective decision rules, which are consistent with rationality, for example stochastic dominance rules. But, as can be seen in many research studies in behavioral economics, decision makers do not always act rationally. Rules based on cumulative prospect theory or almost stochastic dominance are relatively new tools which model real choices. Both approaches take into account some behavioral factors. The aim of this paper is to check the consistency of orders of the valuations of random alternatives based on these behavioral rules. The order of the alternatives is generated by a preference relation over the decision set. In this paper, we show that the methodology for creating rankings based on total orders can be used for the preference relations considered, because they enable comparison of all the elements in a set of random alternatives. For almost second degree stochastic dominance, this is possible due to its particular properties, which stochastic dominance does not possess. (original abstract

Relationship between Omega Function and Stochastic Dominance

Dominacje stochastyczne są relacjami porządku częściowego w zbiorze losowych wariantów decyzyjnych, podobnie jak relacja dominacji oparta na zaproponowanej przez Keatinga i Shadwicka w 2002 roku funkcji omega, służącej ocenie i uporządkowaniu wariantów inwestycyjnych pod kątem ich efektywności. Celem artykułu jest zbadanie zgodności porządku względem dominacji stochastycznych i funkcji omega oraz przedstawienie zależności między tymi kryteriami.Stochastic dominance is a partial order in the set of random decision alternatives. Similarly, a partial order is the relation based on omega function proposed in 2002 by Keating and Shadwick, which is used as a performance measure for the valuation and ordering of investment alternatives. The purpose of this article is to examine the consistency between the ordering according to stochastic dominance and the ordering according to omega function. We also present relationships between these criteria

An evaluation of the selected mathematical competence of the first-year students of economic studies

In Poland, since 1985 when the matura exam in mathematics was no longer compulsory, low-level of math skills and poor learning results have been constantly talked about. The academic community warned that young people were massively avoiding the technical, mathematical fields of study and fields with mathematics as a compulsory subject. We are seeing a constantly decreasing level of mathematical knowledge of first-year students, and sometimes even their ignorance of the elementary issues, basic concepts or an awkwardness in performing calculations. The situation would radically change after the reintroduction of the compulsory matura exam in mathematics in 2010. This article presents the results of the evaluation of the mathematical competence of students (who were obliged to pass the matura exam in mathematics). The evaluation was carried out every year at the beginning of the first year of the economic undergraduate studies during 2012-2014. We have analyzed the level of mathematical competence in the area of knowledge and skills over the subsequent years as well as the knowledge of selected content from the core curriculum of mathematics taught in upper-secondary schools