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Axioms
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Advances in Financial Mathematics and Stochastic Processes
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Advances in Financial Mathematics and Stochastic Processes

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 31 October 2026 | Viewed by 2587

Special Issue Editor

Dr. Geonwoo Kim

E-Mail Website
Guest Editor
School of Liberal Arts, Seoul National University of Science and Technology (SNUST), Seoul, Republic of Korea
Interests: option pricing; mathematical models in finance
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As the complexity of financial markets and systems increases, do does the importance of mathematical models and methodologies. In recent years, financial mathematics has evolved through utilizing various mathematical tools such as stochastic differential equations, time series analysis, machine learning, and big data analytics to model and analyze financial phenomena.

This Special Issue aims to focus on the latest theoretical developments in financial mathematics and their applications in real financial markets, providing a platform for researchers from academia and industry to share their latest research results and practical insights. In addition to developments in traditional financial mathematics methodologies, we also aim to explore the future direction of financial mathematics by including research on the applications of new technologies such as artificial intelligence, quantum computing, and blockchain.

 This Special Issue includes, but is not limited to, the following topics:

  • Financial Stochastic Processes: Stochastic differential equations, jump-diffusion processes, stochastic volatility model.
  • Derivative Pricing and Risk Management: New pricing models, risk measurement methodologies, hedging strategies, exotic options.
  • Portfolio Optimization and Asset Allocation: Multi-objective optimization, robust optimization, dynamic asset allocation.
  • Financial Time Series Analysis: Non-stationary time series, multivariate time series, long-range dependence modeling.
  • Financial Machine Learning: Deep learning-based financial prediction, reinforcement learning for trading, text mining.
  • Systemic Risk and Financial Networks: Financial connectedness, contagion effects, network risk modeling.
  • Mathematical Modeling of Sustainable Finance: ESG risk measurement, climate finance, impact investment evaluation.
  • Latest Techniques in Computational Finance: Monte Carlo methods, finite difference methods, quantum algorithm.

I look forward to receiving your contributions.

Dr. Geonwoo Kim
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 250 words) can be sent to the Editorial Office for assessment.

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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • derivative pricing
  • mathematical models
  • financial mathematics
  • stochastic volatility models
  • jump-diffusion models
  • credit risk
  • machine learning
  • portfolio optimization
  • time series
  • computational finance

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

Published Papers (4 papers)

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Research

23 pages, 369 KB  
Article
Boundary Non-Crossing Probabilities as Functionals of the Deterministic Variance Clock
by Tristan Guillaume
Axioms 2026, 15(5), 321; https://doi.org/10.3390/axioms15050321 - 29 Apr 2026
Viewed by 273
Abstract
We study finite-horizon first-passage time and boundary non-crossing probabilities for Gaussian martingales, viewed as continuous local martingales obtained by running Brownian motion on a deterministic variance clock associated with deterministic volatility. Our aim is to quantify how the associated survival probability changes when [...] Read more.
We study finite-horizon first-passage time and boundary non-crossing probabilities for Gaussian martingales, viewed as continuous local martingales obtained by running Brownian motion on a deterministic variance clock associated with deterministic volatility. Our aim is to quantify how the associated survival probability changes when the variance clock is perturbed. Using a deterministic time change representation, we reduce the problem to a Brownian boundary-crossing problem with a transformed horizon and a transformed boundary. This allows us to combine time change arguments with recent differentiability results for boundary-crossing probabilities. Under suitable regularity assumptions, we derive a first-order sensitivity formula with respect to the variance clock. The derivative splits naturally into two components: one produced by the deformation of the transformed boundary and one produced by the variation of the terminal transformed horizon. Several explicit examples are provided, including affine barriers and nonlinear deterministic clocks. These examples show in particular that, for nonconstant boundaries, redistributing variance over calendar time can change the finite-horizon survival probability even when the terminal variance is kept fixed. Full article
(This article belongs to the Special Issue Advances in Financial Mathematics and Stochastic Processes)
12 pages, 273 KB  
Article
The Fréchet–Newton Scheme for SV-HJB: Stability Analysis via Fixed-Point Theory
by Mehran Paziresh, Karim Ivaz and Mariyan Milev
Axioms 2026, 15(2), 83; https://doi.org/10.3390/axioms15020083 - 23 Jan 2026
Viewed by 504
Abstract
This paper investigates the optimal portfolio control problem under a stochastic volatility model, whose dynamics are governed by a highly nonlinear Hamilton–Jacobi–Bellman equation. We employ a separable value function and introduce a novel exponential approximation technique to simplify the nonlinear terms of the [...] Read more.
This paper investigates the optimal portfolio control problem under a stochastic volatility model, whose dynamics are governed by a highly nonlinear Hamilton–Jacobi–Bellman equation. We employ a separable value function and introduce a novel exponential approximation technique to simplify the nonlinear terms of the auxiliary function. The simplified HJB equation is solved numerically using the advanced Fréchet–Newton method, which is known for its rapid convergence properties. We rigorously analyze the numerical outcomes, demonstrating that the iterative sequence converges quickly to the trivial fixed point (g*=1) under zero risk and zero excess return conditions. This convergence is mathematically justified through rigorous functional analysis, including the principles of contraction mapping and the Kantorovich theorem, which validate the stability and efficiency of the proposed numerical scheme. The results offer theoretical insight into the behavior of the HJB equation in simplified solution spaces. Full article
(This article belongs to the Special Issue Advances in Financial Mathematics and Stochastic Processes)
20 pages, 2273 KB  
Article
The Optimal Robust Investment Problem in the Foreign Stock Market of an Ambiguity-Averse Insurer
by Linlin Tian, Yixuan Tian and Xiaoyi Zhang
Axioms 2026, 15(1), 30; https://doi.org/10.3390/axioms15010030 - 29 Dec 2025
Viewed by 354
Abstract
To address the need for robust investment strategies in an increasingly uncertain global market, this study focuses on an ambiguity-averse insurer facing exchange rate uncertainty while investing in a foreign stock market. The insurer’s surplus is modeled via a classical compound Poisson process, [...] Read more.
To address the need for robust investment strategies in an increasingly uncertain global market, this study focuses on an ambiguity-averse insurer facing exchange rate uncertainty while investing in a foreign stock market. The insurer’s surplus is modeled via a classical compound Poisson process, and exchange rate dynamics are captured using an Ornstein–Uhlenbeck process for the drift component. Within the framework of maximizing expected exponential utility of terminal wealth, we derive and solve the Hamilton–Jacobi–Bellman equation to characterize the optimal investment strategy and the associated value function. Finally, a numerical example illustrates how varying model parameters influences the insurer’s optimal investment behavior. Full article
(This article belongs to the Special Issue Advances in Financial Mathematics and Stochastic Processes)
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13 pages, 277 KB  
Article
Vulnerable Option Pricing Under the 4/2 Stochastic Volatility Model
by Geonwoo Kim
Axioms 2026, 15(1), 3; https://doi.org/10.3390/axioms15010003 - 22 Dec 2025
Viewed by 716
Abstract
In this paper, we study the pricing of vulnerable options, which are exposed to the option issuer’s default risk. We develop a pricing framework that integrates a reduced-form model for default risk with the 4/2 stochastic volatility model for the underlying asset. A [...] Read more.
In this paper, we study the pricing of vulnerable options, which are exposed to the option issuer’s default risk. We develop a pricing framework that integrates a reduced-form model for default risk with the 4/2 stochastic volatility model for the underlying asset. A feature of our model is the correlation between the issuer’s default intensity and the systematic component of the stochastic volatility. Using the characteristic function method and properties of the Grasselli transform, we derive an analytical pricing formula for a European vulnerable call option. Finally, we conduct numerical experiments to illustrate the impact of significant parameters, such as the recovery rate, default intensity, and the specific parameters of the 4/2 model. The results show that the 4/2 model component, which distinguishes it from the standard Heston model, has a significant effect on option prices. Full article
(This article belongs to the Special Issue Advances in Financial Mathematics and Stochastic Processes)
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