Latest Advances in Mathematical Economics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: 15 June 2024 | Viewed by 2382

Special Issue Editors


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Guest Editor
Department of Economics, University of Thessaly, 28th Octovriou st. 78, 38333 Volos, Greece
Interests: computational mathematics; symbolic computations; computer algebra systems; data visualization; information visualization; graph theory; economic networks; mathematical education with new technologies

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Guest Editor
Department of Economics, National and Kapodistrian University of Athens, Sofokleous 1, 10533 Athens, Greece
Interests: nonlinear systems; mathematical systems theory; dynamical economics

E-Mail Website
Guest Editor
Department of Economics, University of Thessaly, 28th Octovriou st. 78, 38333 Volos, Greece
Interests: nonlinear dynamical systems; economic dynamics; stability theory

Special Issue Information

Dear Colleagues,

The purpose of this Special Issue is to publish the work of mathematicians interested in studying a number of mathematical methods to represent theories and analyze problems in economics. Some of the potential topics of papers could be well-understood problems from a novel computer-aided perspective, whereas others could present new and challenging mathematical problems.

The potential topics including, but not limited to, the following will be considered for publication: 

  • Revisiting the research of classical economic problems, replication studies of established papers, and/or classical models; 
  • Solutions for differential and integral calculus, difference and differential equations, matrix algebra, and mathematical programming in new, innovative computational environments;
  • ICT tools for teaching mathematical economics courses and evaluating students’ theoretical and practical knowledge;
  • The recent results in graph theory for problems that represent and explain economic behavior, income, and wealth distribution;
  • Games theory;
  • Computational and algorithmic methods in economics;
  • The formation and analysis of input–output structures with matrix algebra formulations;
  • Topological issues answering open questions regarding the well-posedness of problems, and theorems on the existence of a solution, i.e., of a time-dependent equilibrium, and/or the uniqueness of a solution, i.e., of a stationary equilibrium.

Dr. Kyriaki Tsilika
Prof. Dr. Stelios Kotsios
Dr. Loukas Zachilas
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • stability
  • convergence issues
  • analytical solutions
  • coefficient matrices
  • computational and algorithmic methods

Published Papers (2 papers)

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Research

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12 pages, 273 KiB  
Article
Feedback Control Techniques for a Discrete Dynamic Macroeconomic Model with Extra Taxation: An Algebraic Algorithmic Approach
by Stelios Kotsios
Mathematics 2023, 11(19), 4213; https://doi.org/10.3390/math11194213 - 9 Oct 2023
Viewed by 625
Abstract
In this paper, a model matching feedback law design technique is applied to a macroeconomical model. We calculate, using computational algebra methodology, which paths of government expenditure and extra taxation will lead the system to a desired dynamic behavior. The solution is based [...] Read more.
In this paper, a model matching feedback law design technique is applied to a macroeconomical model. We calculate, using computational algebra methodology, which paths of government expenditure and extra taxation will lead the system to a desired dynamic behavior. The solution is based on algebraic methods and the development, in computer algebra software, of appropriate symbolic algorithms that produce a class of feedback laws as solutions. A method for solving a linear algebraic system of polynomials equations is provided, as well as its application to the feedback law design. Full article
(This article belongs to the Special Issue Latest Advances in Mathematical Economics)

Review

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21 pages, 14317 KiB  
Review
Exploring the Contributions to Mathematical Economics: A Bibliometric Analysis Using Bibliometrix and VOSviewer
by Kyriaki Tsilika
Mathematics 2023, 11(22), 4703; https://doi.org/10.3390/math11224703 - 20 Nov 2023
Cited by 1 | Viewed by 1279
Abstract
From Cournot, Walras, and Pareto’s research to what followed in the form of marginalist economics, chaos theory, agent-based modeling, game theory, and econophysics, the interpretation and analysis of economic systems have been carried out using a broad range of higher mathematics methods. The [...] Read more.
From Cournot, Walras, and Pareto’s research to what followed in the form of marginalist economics, chaos theory, agent-based modeling, game theory, and econophysics, the interpretation and analysis of economic systems have been carried out using a broad range of higher mathematics methods. The evolution of mathematical economics is associated with the most productive and influential authors, sources, and countries, as well as the identification of interactions between the authors and research topics. Bibliometric analysis provides journal-, author-, document-, and country-level metrics. In the present study, a bibliometric overview of mathematical economics came from a screening performed in September 2023, covering the timespan 1898–2023. About 6477 documents on mathematical economics were retrieved and extracted from the Scopus academic database for analysis. The Bibliometrix package in the statistical programming language R was employed to perform a bibliometric analysis of scientific literature and citation data indexed in the Scopus database. VOSviewer (version 1.6.19) was used for the visualization of similarities using several bibliometric techniques, including bibliographic coupling, co-citation, and co-occurrence of keywords. The analysis traced the most influential papers, keywords, countries, and journals among high-quality studies in mathematical economics. Full article
(This article belongs to the Special Issue Latest Advances in Mathematical Economics)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Multi-user water allocation under deep uncertainty and model misspecification concerns
Authors: I. Mourtos; G Papayiannis; P. Xepapadeas; A. Xepapadeas; A. Yannacopoulos.
Affiliation: Department of Statistics Athens University Economics and Business
Abstract: We study a water allocation problem over time from two sources, surface water and underground water to three users, industrial, residential, and agricultural when the users or a water regulator are uncertainty averse and have misspecifications concerns regarding water dynamics from each source. Deep uncertainty in water dynamics is associated with uncertain weather conditions, which cannot be captured by a unique probability distribution, and which are further intensified by climate change. We formulate the problem in the context of multi agent resource allocation problem in which allocation to users can be implemented by sequential serial dictatorship or simultaneous cooperative or non-cooperative approaches. Deep uncertainty and model misspecification is modeled by considering a benchmark model for water dynamics which is surrounded by other possible models whose distance from the benchmark is measured by Kullback-Leibler entropy. Alternative models are contained in an entropy ball with center the benchmark model and radius the maximum distance between the benchmark and the alternative model that agents are willing to consider. Users cannot determine with existing data, which is the true model - benchmark or alternatives - within the ball, and this introduces ambiguity in the decision process. Assuming that agents are ambiguity averse we solve the problem in a maxmin expected utility framework by using robust control methods. We compare, serial dictatorship, cooperative and non-cooperative water path allocations as well as individual and global utility associated with each approach and provide policy recommendations

Title: A Microeconomic Model Evaluating the Dynamic Behaviour of A Two Stage Supply Chain with Autocorrelated Demand under a VMI Program
Authors: Ilias S. Kevork; Christos N. Tziourtzioumis
Affiliation: Department of Economics, University of Thessaly, Greece
Abstract: Collaborative mechanisms among supply chain members, when they are expressed by some form of information sharing, are important to the effective performance of supply chains. In this paper, we develop a microeconomic model for a two stage supply chain which relates demand forecasting and inventory performance. Particularly, assuming that (a) demand at the retailer (downstream member) is modelled by an ARMA (1,1) process, (b) the lead time is fixed in both members and (c) an order- up-to (OUT) level inventory policy is adopted by the two members of the chain, the benefits of two information sharing scenarios are investigated. The first, known as No Information Sharing (NIS) scenario, considers that the supplier (upstream member) does not have access to any information concerning demand data and the demand model with its parameter values being used by the retailer. The second scenario requires that the supplier, not only has access to all information concerning the demand faced by the retailer, but also is responsible for managing the inventory of retailer through a “Vendor Managed Inventory (VMI)” program. In the aforementioned context, initially we derive mathematically, through stochastic analysis of time series, the values of key-criteria, such as the bullwhip ratio, the average on-hand inventory level, and holding and shortage cost, as functions of the duration of lead-time and the parameters of exogenous and endogenous demand models being used by the retailer and the supplier respectively. Finally, we specify the conditions under which the adoption of a VMI collaboration program is beneficial for both members of the supply chain.

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