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Massimo Angrisani, Giovanni di Nella, Cinzia di Palo and Augusto Pianese

Abstract

This paper deals with the problem of the optimal rate of return to be paid by a defined contribution pension system to its participants’ savings, namely the rate that achieves the goal of the most favorable returns on their contributions jointly with the sustainability of the pension system.

We consider defined contribution pension systems provided with a funded component, and for their study we use the “theory of the logical sustainability of pension systems” already developed in several previous works. In this paper, we focus on pension systems in a demographically stable state, whereas the productivity of the active participants and the financial rate of return on the pension system’s fund, rates that constitute the “ingredients” of the optimal rate of return on contributions, are modeled by two stochastic processes.

We show that the decisional rule defining the optimal rate of return on contributions is optimal in the sense that it is effective in terms of sustainability, and also efficient in the sense that if the system pays to its participants’ contributions a rate of return that is either higher or lower than the one provided by the rule, then the pension system becomes unsustainable or overcapitalized, respectively.

Open access

Justyna Brzezińska

Abstract

Visualization in research process plays a crucial role. There are several advanced plots for visualizing categorical data, such as mosaic, association, double-decker, sieve or fourfold plot that are based on the graphical presentation of residuals in a contingency table. In this paper we present new methods for visualizing categorical data such as rmb, fluctile and scpcp plot available in extracat package in R. This package provides a well-structured representation of categorical data and allows for a detailed presentation of the relationship between categories in terms of proportions. We describe rmb, fluctile and cpcp. Those plots are based on the concept of multiple bar charts, a fluctuation diagram from a multidimensional table and parallel coordinates respectively. Such plots are mostly used for a visualization of a contingency table or a data frame; they can also be used for exploratory analysis and allows for a graphical presentation even for a high number of variables [Pilhöfer, Unwin 2013]. All the calculations and plots are obtained using R software.

Open access

Justyna Brzezińska

Abstract

Economic poverty is one of the more common and complex problems in the modern world, as well as in Poland. This is a complex and multidimensional phenomenon, and therefore there is no single universally valid definition of poverty. This article presents a statistical analysis of economic poverty in Poland based on real data from the Central Statistical Office of Poland. An in-depth statistical analysis of the social situation of Poles will be presented, as well as an attempt to examine interdependencies in the occurrence of various forms of poverty and social exclusion in Poland. In the article, several multivariate statistical methods are presented together with the graphical presentation of results. We present a correspondence analysis with a perception map, as well as the advanced modern visualizing tool for categorical data. All the calculations were conducted using R software.

Open access

Michał Brzozowski and Joanna Siwińska-Gorzelak

Abstract

The aim of this paper is to shed light on the public and private sector interdependencies in the international financial market. Using annual data on sovereign and private sector external indebtedness for 95 emerging and developing countries in the 1970-2012 period it looks at the relationship between the level and structure of public external debt and the likelihood of private sector entry in international bond and loan markets. The private sector entry in the offshore loans and bonds markets is shown to be conditional on the amount of public sector external debt. The relationship is complex but in general the saturation of the financial market with external government liabilities renders the private sector entry into the bonds’ market more difficult.

Open access

Jan Baran

Abstract

This paper analyses changes in overeducation incidence in Poland in 2006‑2014. It finds that a rise in number of tertiary educated workers outpaced an increase in number of jobs requiring tertiary education, which resulted in a substantial growth of overeducation incidence. The overeducation increase was driven mainly by mild overeducation rather than severe overeducation. Overeducated workers are usually young with little job experience. Women are found at lower risk of severe overeducation compared to men, but relatively more at risk of mild overeducation. A low risk of overeducation is associated with having studied technical and health programmes.

Open access

Witold Rzymowski and Agnieszka Surowiec

Abstract

Selected econometric methods of modelling the world’s population size based on historical data are presented in the paper. Periodical variables were used in the models proposed in the paper. Moreover, a logistic-type function was used in modelling. The purpose of the paper was to obtain a model describing the world’s population with the lowest possible maximal relative error and possibly the longest period of durability. In this work, 13,244 models from three families models were analyzed. Only a small part of such a large number of models satisfies the conditions of stability. The method of modelling the world’s population size allows to obtain models with maximal relative errors not exceeding 0.5%. Selected models were used to prediction of the world’s population up to 2050. The obtained results were compared with data published by the Organisation for Economic Co-operation and Development.

Open access

Natalia Nehrebecka

Abstract

The aim of the article is to compare models on a train and validation sample, which will be created using logistic regression and Support Vector Machine (SVM) and will be used to assess the credit risk of non-financial enterprises. When creating models, the variables will be subjected to the transformation of the Weight of Evidence (WoE), the number of potential predictions will be reduced based on the Information Value (IV) statistics. The quality of the models will be assessed according to the most popular criteria such as GINI statistics, Kolmogorov-Smirnov (K-S) and Area Under Receiver Operating Characteristic (AUROC). Based on the results, it was found that there are significant differences between the logistic regression model of discriminatory character and the SVM for the model sample. In the case of a validation sample, logistic regression has the best prognostic capability. These analyses can be used to reduce the risk of negative effects on the financial sector.

Open access

Sabir Hussain

Abstract

In this paper, we initiate and explore the interesting characterizations and properties of fuzzy soft almost soft continuous mappings in fuzzy soft classes. We also study and discuss the notions of fuzzy soft almost soft open(closed) mappings. Moreover the characterizations of composition of two fuzzy soft almost soft mappings are also studied. We hope that the endings in this paper will be useful for the researchers working in the fields such as fuzzy control systems, fuzzy automata, fuzzy logic, information systems and decision making problems

Open access

Dominika Machowska

Abstract

The paper investigates the optimal allocation between defensive and offensive advertising efforts in a dynamic, growing market in which two companies are competing for market share. The study described in this paper extends the existing literature on dynamic advertising competition by considering a market that is in the growth phase and by including the heterogeneous decay rate of market share. A modified Lanchester is employed to describe the dynamics of market share by model. The goal of companies operating in this domain is to maximize their profits over a finite decision horizon. Based on the differential game approach the Markovian Nash strategies for offensive and defensive advertising activities are determined. Additionally, an analysis of the extent to which this solution is sensitive to changes in potential market and the rate of customer churn is made.

Open access

Aleksander Kaczmarek, Krzysztof Przybyszewski, Dorota Rutkowska and Honorata Sosnowska

Abstract

The aim of this paper is to check whether mathematical competences influence some manifestations of bounded rationality. A special example of bounded rationality called “framing effect” is dealt with to analyze empirically the thesis that mathematical competences and cognitive effort may reduce the framing effect. Two kinds of cognitive effort: probabilistic and deductive are analysed. Experiments were conducted using samples of Polish students, both mathematically and business oriented. As an example of a framing situation an example called “Asian disease”, (the first analyzed and the most popular example of the framing effect), is considered. The thesis that a mathematical background may diminish the occurrence of the framing effect was partly confirmed.