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Mathematics
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Modern Trends in Mathematics, Probability and Statistics for Finance
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Modern Trends in Mathematics, Probability and Statistics for Finance

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E5: Financial Mathematics".

Deadline for manuscript submissions: 30 April 2026 | Viewed by 2230

Special Issue Editor

Dr. Nguyet Nguyen

E-Mail Website
Guest Editor
Department of Mathematics & Statistics, Youngstown State University, Youngstown, OH 44555, USA
Interests: mathematical models in finance; mathematical modelling and simulation; numerical analysis; applied mathematics; numerical modeling financial markets; computational finance

Special Issue Information

Dear Colleagues,

Welcome to this Special Issue dedicated to exploring the intricate relationship between mathematics, probability, and statistics in the realm of finance. In today's fast-paced and ever-evolving financial landscape, understanding the underlying mathematical principles, probabilistic models, and statistical methods is crucial for making informed decisions, managing risk, and uncovering new avenues for financial innovation.

This issue brings together a collection of cutting-edge research articles and insightful contributions from leading experts in the field. From advanced mathematical modeling techniques to sophisticated probabilistic frameworks, and from empirical studies to theoretical advancements, each article offers valuable insights into the application of mathematical and statistical methodologies in finance.

Topics covered in this Special Issue include, but are not limited to, the following:

  • Stochastic option pricing models;
  • Derivative pricing and hedging;
  • Modeling and pricing in insurance;
  • Portfolio optimization;
  • Optimal investment;
  • Risk management;
  • Models for credit risk;
  • Value at risk (VaR) models;
  • Financial time series analysis;
  • Optimal stopping in mathematical finance;
  • High-frequency trading strategies;
  • Machine learning applications in finance.

By delving into these topics, we aim to provide readers with a comprehensive understanding of the mathematical and statistical tools that underpin modern finance and their practical implications for investment, risk management, and financial decision-making.

We hope that this Special Issue will serve as a valuable resource for researchers, practitioners, and students alike, fostering further exploration and innovation at the intersection of mathematics, probability, and statistics in finance.

Dr. Nguyet Nguyen
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

  • pricing models
  • portfolio optimization
  • risk management
  • financial time series analysis
  • high-frequency trading strategies
  • optimal stopping
  • stochastic games
  • machine learning

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

Published Papers (3 papers)

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Research

38 pages, 1461 KB  
Article
Mixed ABMs for NDC Pension Schemes in the Presence of Demographic and Economic Uncertainty
by Jacopo Giacomelli and Massimiliano Menzietti
Mathematics 2025, 13(21), 3454; https://doi.org/10.3390/math13213454 (registering DOI) - 29 Oct 2025
Abstract
The crisis of pension systems based on pay-as-you-go (PAYG) financing has led to the introduction in some countries, including Italy, of so-called notional defined contribution (NDC) pension accounts. These systems mimic the functioning of defined contribution systems in benefit calculations while remaining based [...] Read more.
The crisis of pension systems based on pay-as-you-go (PAYG) financing has led to the introduction in some countries, including Italy, of so-called notional defined contribution (NDC) pension accounts. These systems mimic the functioning of defined contribution systems in benefit calculations while remaining based on PAYG financing. Despite many appealing features, NDC accounts cannot automatically guarantee a system’s financial sustainability in the presence of demographic or economic fluctuations. The literature proposes automatic balance mechanisms (ABMs) of the notional rate applied to notional accounts and an indexation rate applied to pensions. ABMs may be based on two indicators: the liquidity ratio or the solvency ratio. Such ABMs may strengthen a system’s financial sustainability but may produce significant fluctuations in the adjusted notional rate, thereby undermining the social adequacy of the system. In this work, we introduce a mixed ABM based on both the liquidity ratio and solvency ratio and identify the optimal combination that guarantees financial sustainability of the system and, at the same time, maximizes the return paid to the participants at fixed levels of confidence. The numerical results show the advantages of a mixed mechanism over those based on a single indicator. Indeed, although the results depend on the system’s initial conditions and the different ABM configurations tested (16 in total), some common patterns emerge across the solutions. A solvency ratio-based ABM maximizes social utility, while a liquidity ratio-based one ensures financial stability. Although not optimal for either criterion, the ABM that mixes the liquidity ratio and solvency ratio in proportions ranging from 60–40% to 50–50% emerges from our numerical simulations as the best compromise to achieve these two objectives jointly. Full article
(This article belongs to the Special Issue Modern Trends in Mathematics, Probability and Statistics for Finance)
25 pages, 1288 KB  
Article
An Analysis of Implied Volatility, Sensitivity, and Calibration of the Kennedy Model
by Dalma Tóth-Lakits, Miklós Arató and András Ványolos
Mathematics 2025, 13(21), 3396; https://doi.org/10.3390/math13213396 - 24 Oct 2025
Viewed by 239
Abstract
The Kennedy model provides a flexible and mathematically consistent framework for modeling the term structure of interest rates, leveraging Gaussian random fields to capture the dynamics of forward rates. Building upon our earlier work, where we developed both theoretical results—including novel proofs of [...] Read more.
The Kennedy model provides a flexible and mathematically consistent framework for modeling the term structure of interest rates, leveraging Gaussian random fields to capture the dynamics of forward rates. Building upon our earlier work, where we developed both theoretical results—including novel proofs of the martingale property, connections between the Kennedy and HJM frameworks, and parameter estimation theory—and practical calibration methods, using maximum likelihood, Radon–Nikodym derivatives, and numerical optimization (stochastic gradient descent) on simulated and real par swap rate data, this study extends the analysis in several directions. We derive detailed formulas for the volatilities implied by the Kennedy model and investigate their asymptotic properties. A comprehensive sensitivity analysis is conducted to evaluate the impact of key parameters on derivative prices. We implement an industry-standard Monte Carlo method, tailored to the conditional distribution of the Kennedy field, to efficiently generate scenarios consistent with observed initial forward curves. Furthermore, we present closed-form pricing formulas for various interest rate derivatives, including zero-coupon bonds, caplets, floorlets, swaplets, and the par swap rate. A key advantage of these results is that the formulas are expressed explicitly in terms of the initial forward curve and the original parameters of the Kennedy model, which ensures both analytical tractability and consistency with market-observed data. These closed-form expressions can be directly utilized in calibration procedures, substantially accelerating multidimensional nonlinear optimization algorithms. Moreover, given an observed initial forward curve, the model provides significantly more accurate pricing formulas, enhancing both theoretical precision and practical applicability. Finally, we calibrate the Kennedy model to market-observed caplet prices. The findings provide valuable insights into the practical applicability and robustness of the Kennedy model in real-world financial markets. Full article
(This article belongs to the Special Issue Modern Trends in Mathematics, Probability and Statistics for Finance)
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41 pages, 6841 KB  
Article
Distributionally Robust Multivariate Stochastic Cone Order Portfolio Optimization: Theory and Evidence from Borsa Istanbul
by Larissa Margerata Batrancea, Mehmet Ali Balcı, Ömer Akgüller and Lucian Gaban
Mathematics 2025, 13(15), 2473; https://doi.org/10.3390/math13152473 - 31 Jul 2025
Viewed by 1216
Abstract
We introduce a novel portfolio optimization framework—Distributionally Robust Multivariate Stochastic Cone Order (DR-MSCO)—which integrates partial orders on random vectors with Wasserstein-metric ambiguity sets and adaptive cone structures to model multivariate investor preferences under distributional uncertainty. Grounded in measure theory and convex analysis, DR-MSCO [...] Read more.
We introduce a novel portfolio optimization framework—Distributionally Robust Multivariate Stochastic Cone Order (DR-MSCO)—which integrates partial orders on random vectors with Wasserstein-metric ambiguity sets and adaptive cone structures to model multivariate investor preferences under distributional uncertainty. Grounded in measure theory and convex analysis, DR-MSCO employs data-driven cone selection calibrated to market regimes, along with coherent tail-risk operators that generalize Conditional Value-at-Risk to the multivariate setting. We derive a tractable second-order cone programming reformulation and demonstrate statistical consistency under empirical ambiguity sets. Empirically, we apply DR-MSCO to 23 Borsa Istanbul equities from 2021–2024, using a rolling estimation window and realistic transaction costs. Compared to classical mean–variance and standard distributionally robust benchmarks, DR-MSCO achieves higher overall and crisis-period Sharpe ratios (2.18 vs. 2.09 full sample; 0.95 vs. 0.69 during crises), reduces maximum drawdown by 10%, and yields endogenous diversification without exogenous constraints. Our results underscore the practical benefits of combining multivariate preference modeling with distributional robustness, offering institutional investors a tractable tool for resilient portfolio construction in volatile emerging markets. Full article
(This article belongs to the Special Issue Modern Trends in Mathematics, Probability and Statistics for Finance)
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