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Mathematics
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Recent Advances in Mathematical Methods for Economics
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Recent Advances in Mathematical Methods for Economics

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

Deadline for manuscript submissions: 30 November 2024 | Viewed by 5614

Special Issue Editor

Dr. Luca Piccoli

E-Mail Website
Guest Editor
Department of Sociology and Social Research, University of Trento, 38122 Trento, Italy
Interests: labor economics; public economics; family economics; risky behaviors

Special Issue Information

Dear Colleagues,

Advances in mathematical methods have difficulties translating into economic modeling. The economic scientific community has largely continued to base their research and modeling on traditional mathematical tools, disregarding many possibly fruitful advances in mathematical methods.

This Special Issue aims to fill this gap through collecting original research involving the application of recently developed mathematical methods in any field of economics, from microeconomics to macroeconomics, from finance to public economics, from labor and behavioral economics to health economics, etc. The submission of reviews on recent developments in mathematical methods in specific sectors of economics is particularly welcome. The baseline message this Special Issue hopes to promote is that keeping up with advances in mathematics is crucially important for economists. In this sense, submissions should ideally propose or review recent mathematical methods for solving economic problems or modeling issues that cannot be dealt with using traditional mathematical tools.

Dr. Luca Piccoli
Guest Editor

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

  • mathematical economics
  • optimization
  • model solution
  • microeconomics
  • macroeconomics
  • financial economics
  • public economics
  • labor economics
  • behavioral economics

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (4 papers)

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Research

27 pages, 830 KiB  
Article
Leveraging Bayesian Quadrature for Accurate and Fast Credit Valuation Adjustment Calculations
by Noureddine Lehdili, Pascal Oswald and Othmane Mirinioui
Mathematics 2024, 12(23), 3779; https://doi.org/10.3390/math12233779 (registering DOI) - 29 Nov 2024
Viewed by 257
Abstract
Counterparty risk, which combines market and credit risks, gained prominence after the 2008 financial crisis due to its complexity and systemic implications. Traditional management methods, such as netting and collateralization, have become computationally demanding under frameworks like the Fundamental Review of the Trading [...] Read more.
Counterparty risk, which combines market and credit risks, gained prominence after the 2008 financial crisis due to its complexity and systemic implications. Traditional management methods, such as netting and collateralization, have become computationally demanding under frameworks like the Fundamental Review of the Trading Book (FRTB). This paper explores the combined application of Gaussian process regression (GPR) and Bayesian quadrature (BQ) to enhance the efficiency and accuracy of counterparty risk metrics, particularly credit valuation adjustment (CVA). This approach balances excellent precision with significant computational performance gains. Focusing on fixed-income derivatives portfolios, such as interest rate swaps and swaptions, within the One-Factor Linear Gaussian Markov (LGM-1F) model framework, we highlight three key contributions. First, we approximate swaption prices using Bachelier’s formula, showing that forward-starting swap rates can be modeled as Gaussian dynamics, enabling efficient CVA computations. Second, we demonstrate the practical relevance of an analytical approximation for the CVA of an interest rate swap portfolio. Finally, the combined use of Gaussian processes and Bayesian quadrature underscores a powerful synergy between precision and computational efficiency, making it a valuable tool for credit risk management. Full article
(This article belongs to the Special Issue Recent Advances in Mathematical Methods for Economics)
17 pages, 4105 KiB  
Article
A Copula-Based Bivariate Composite Model for Modelling Claim Costs
by Girish Aradhye, George Tzougas and Deepesh Bhati
Mathematics 2024, 12(2), 350; https://doi.org/10.3390/math12020350 - 22 Jan 2024
Cited by 1 | Viewed by 1072
Abstract
This paper aims to develop a new family of bivariate distributions for modelling different types of claims and their associated costs jointly in a flexible manner. The proposed bivariate distributions can be viewed as a continuous copula distribution paired with two marginals based [...] Read more.
This paper aims to develop a new family of bivariate distributions for modelling different types of claims and their associated costs jointly in a flexible manner. The proposed bivariate distributions can be viewed as a continuous copula distribution paired with two marginals based on composite distributions. For expository purposes, the details of one of the proposed bivarite composite distributions is provided. The dependence measures for the resulting bivariate copula-based composite distribution are studied, and its fitting is compared with other bivariate composite distributions and existing bivariate distributions. The parameters of the proposed bivariate composite model are estimated via the inference functions for margins (IFM) method. The suitability of the proposed bivariate distribution is examined using two real-world insurance datasets, namely the motor third-party liability (MTPL) insurance dataset and Danish fire insurance dataset. Full article
(This article belongs to the Special Issue Recent Advances in Mathematical Methods for Economics)
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12 pages, 436 KiB  
Article
A Markov Decision Process with Awareness and Present Bias in Decision-Making
by Federico Bizzarri, Chiara Mocenni and Silvia Tiezzi
Mathematics 2023, 11(11), 2588; https://doi.org/10.3390/math11112588 - 5 Jun 2023
Cited by 1 | Viewed by 1789
Abstract
We propose a Markov Decision Process Model that blends ideas from Psychological research and Economics to study decision-making in individuals with self-control problems. We have borrowed a dual-process of decision-making with self-awareness from Psychological research, and we introduce present bias in inter-temporal preferences, [...] Read more.
We propose a Markov Decision Process Model that blends ideas from Psychological research and Economics to study decision-making in individuals with self-control problems. We have borrowed a dual-process of decision-making with self-awareness from Psychological research, and we introduce present bias in inter-temporal preferences, a phenomenon widely explored in Economics. We allow for both an exogenous and endogenous, state-dependent, present bias in inter-temporal decision-making and explore, by means of numerical simulations, the consequences on well-being emerging from the solution of the model. We show that, over time, self-awareness may mitigate present bias and suboptimal choice behaviour. Full article
(This article belongs to the Special Issue Recent Advances in Mathematical Methods for Economics)
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14 pages, 311 KiB  
Article
On the Curvature Properties of “Long” Social Welfare Functions
by Piera Mazzoleni, Elisa Pagani and Federico Perali
Mathematics 2023, 11(7), 1674; https://doi.org/10.3390/math11071674 - 31 Mar 2023
Viewed by 1426
Abstract
This study characterizes the concavity properties of the Jorgenson and Slesnick’s social welfare function that is likely the most empirically relevant function among the family of “long” welfare functions. We bridge this knowledge gap using the definition of generalized concavity to show the [...] Read more.
This study characterizes the concavity properties of the Jorgenson and Slesnick’s social welfare function that is likely the most empirically relevant function among the family of “long” welfare functions. We bridge this knowledge gap using the definition of generalized concavity to show the conditions necessary for the long social welfare function of interest to be decreasing and quasi-convex with respect to prices. Thanks to this result, “long” social welfare functions with regular curvature can be suitable for applied social welfare analysis and policy evaluations. Full article
(This article belongs to the Special Issue Recent Advances in Mathematical Methods for Economics)
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