<abstract xmlns="http://www.w3.org/1999/xhtml">In several developed countries, the baby boomers will come to retire in the next decades. This problem will threaten the sustainability and the intergenerational equity of mandatory pay-as-you-go pension systems because they will have to drain the “demographic wave” of retirees with a relatively small number of contributors. In this paper, we give the operating method developed on the basis of a general principle, which a defined contribution pension system, in a state of stable sustainability, should adopt to control these issues in the presence of a demographic wave. In the theoretical profile, our approach breaks and overcomes the classical juxtaposition between funded and pay-as-you-go pension schemes, carrying out the integration of the two financial methods.</abstract>

Controlling a demographic wave in defined contribution pension systems

<abstract xmlns="http://www.w3.org/1999/xhtml">Existence of viable trajectories to nonautonomous differential inclusions are proven for time-dependent viability tubes. In the convex case we prove a double-selection theorem and a new Scorza-Dragoni type lemma. Our result also provides a new and palpable proof for the equilibrium form of Kakutani’s fixed point theorem.</abstract>

Duplex selections, equilibrium points, and viability tubes

<abstract xmlns="http://www.w3.org/1999/xhtml">There are numerous attempts to estimate hiking time since the age of the ancient Roman Empire, the new digital era calls for more precise and exact solutions to be implemented in mobile applications. The importance of the topic lies in the fact that route planning algorithms and shortest path problems apply time estimations as cost functions. Our intention is to design a hiking time estimation method that accounts for terrain circumstances as well as personal factors, while the level of accuracy and the simplicity of the algorithm should enable the solution to be utilised in the practice. We refine Tobler’s earlier results to estimate a relation between terrain steepness and hiker’s velocity. Later we use fitted curve to design our novel, personalised hiking time estimation method.</abstract>

Personalised Hiking Time Estimation

<abstract xmlns="http://www.w3.org/1999/xhtml">We provide a two good model of oligopolistic production and trade with one good being commodity money. There is the usual demand function of the consumers for the produced good that producer-sellers face. Each seller is a budget constrained preference maximizer and derives utility (or satisfaction) from consuming bundles comprising commodity money and the produced good. We define a competitive equilibrium strategy profile and a Cournotian equilibrium and show that under our assumptions both exist. We further show that at a competitive equilibrium strategy profile, each seller maximizes profits given his own consumption of the produced good and the price of the produced good, the latter being determined by the inverse demand function. Similarly we show that at a Cournotian the sellers are at a Cournot equilibrium given their own consumption of the produced good. Assuming sufficient differentiability of the cost functions we show that at a competitive equilibrium each seller either sets price equal to marginal cost or exhausts his capacity of production; at a Cournotian equilibrium each seller either sets marginal revenue equal to marginal cost or exhausts his capacity of production. We also study the evolution of Cournotian strategies as the sellers and buyers are replicated. As the number of buyers and sellers go to infinity any sequence of interior symmetric Cournotian equilibrium strategies admits a convergent subsequence, which converges to an interior symmetric competitive equilibrium strategy. In a final section we discuss the Bertrand Edgeworth price setting game and show that a Bertrand Edgeworth equilibrium must be a derived from a competitive equilibrium price. Here we show that if at a symmetric competitive equilibrium, the sellers consume positive quantities of the produced good then the competitive equilibrium cannot be a Bertrand Edgeworth equilibrium. Thus, if at all symmetric competitive equilibria the sellers consume positive amounts of the produced good, then a Bertrand Edgeworth equilibrium simply does not exist.</abstract>

A simple model of production and trade in an oligopolistic market: back to basics

<abstract xmlns="http://www.w3.org/1999/xhtml">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.</abstract>

The optimal rate of return for defined contribution pension systems in a stochastic framework

AHEAD OF PRINT

Volume 30 (2022): Issue 4 (December 2022)

Volume 30 (2022): Issue 3 (October 2022) Special issue dedicated to 70th anniversary of prof. Peter Tallos

Volume 30 (2022): Issue 2 (August 2022)

Volume 30 (2022): Issue 1 (June 2022)

Volume 29 (2020): Issue 1 (December 2020)

Volume 28 (2019): Issue 1 (October 2019)

Volume 27 (2018): Issue 2 (August 2018)

Volume 27 (2018): Issue 1 (July 2018)

Volume 26 (2017): Issue 1 (June 2017)

Volume 25 (2015): Issue 2 (December 2015)

Volume 25 (2015): Issue 1 (September 2015)

Pure Mathematics and Applications

 Pure Mathematics and Applications - section Algebra and Theoretical Computer Science - publishes original high quality articles of international relevance in the two disciplines of algebra and theoretical computer science. Specific topics include (but are not limited to) group and semigroup theory, commutative algebra, computational algebra, poset and lattice theory, linear algebra, theory of automata and formal languages, computational complexity, analysis of algorithms, game theory. In particular, articles in which interactions between algebra and theoretical computer science play a relevant role (i.e. techniques of either discipline are fundamental in obtaining results of the other) will be privileged. As a natural consequence of this fact, one of the disciplines which are more relevant to the journal is discrete mathematics, and more specifically enumerative and algebraic combinatorics, graph theory, discrete tomography, random and exhaustive generation, combinatorial order theory, bioinformatics, matroid theory, combinatorics on words.Papers about high quality applications of combinatorial methods to computer science (especially algorithms, data structures, and criptography), or special issues, completely devoted to a certain contemporary topic of high interest, are also published.  Pure Mathematics and Applications - section Mathematics of Optimization - publishes original research works, surveys, historical and biographical articles primarily on mathematics of optimization. Papers about high quality applications of mathematical methods to decision sciences (especially operations research, economics, games and control theory, actuarial and financial mathematics), or special issues, completely devoted to a certain contemporary topic of high interest are also published.  The journal contains two sections - one devoted to Algebra and Theoretical Computer Science, and second to Mathematics of Optimization. The published articles of the first section focus on algebra and theoretical computer science, with interactions between algebra and theoretical computer science in particular. The second section publishes research works, surveys, historical and biographical articles primarily on mathematics of optimization.  Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process.  Target group  researchers in the fields of algebra and theoretical computer science 