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Risks
Special Issues
New Challenges in Mathematical Finance: From S(P)DEs to Machine Learning
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New Challenges in Mathematical Finance: From S(P)DEs to Machine Learning

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: closed (15 March 2023) | Viewed by 6511

Special Issue Editors

Dr. Luca Di Persio

E-Mail Website1 Website2
Guest Editor
Department of Computer Science, College of Mathematics, University of Verona, Strada le Grazie 15, 37134 Verona, Italy
Interests: stochastic partial differential equations (SPDEs) in both finite and infinite dimensions; asymptotic expansion of finite/infinite integrals; interacting particle systems; random walk in random media; stochastic mean field games with applications in finance; time series analysis with applications in finance; machine learning and mathematical foundations of neural networks with applications in real markets
Special Issues, Collections and Topics in MDPI journals
Dr. Francesco Giuseppe Cordoni

E-Mail Website
Co-Guest Editor
Department of Computer Science, University of Verona - Strada le Grazie, 15 37134 Verona, Italy
Interests: stochastic partial differential equations with applications in finance; stochastic control with applications in finance/industry; theory and implementation of neural networks architectures
Dr. Immacolata Oliva

E-Mail Website
Co-Guest Editor
Department of Methods and Models for Economics, Territory and Finance, Sapienza University of Rome, Rome, Italy
Interests: risk measures with high-frequency data; mathematical approaches to risk measures; stochastic differential equations with jumps in mathematical finance with applications to pricing, hedging and dynamic risk measure’s problems; evaluation of derivatives using stochastic discount factor

Special Issue Information

Dear Colleagues,

Financial markets are currently characterized by an increasing number of challenging tasks which outperform already-obtained results in terms, for example, of standard credit risk measures, interest rates structures analysis, financial scenario forecasting, and related sub-problems. In particular, the enormous mass of data, spanning from micro-economic to macro-economic frameworks, demands the development of a new stochastic-based holistic vision which can re-establish the right grip between mathematical theory and related applied tools as well as between quantitative tasks and their formally correct description/analysis/forecast. Therefore, this Special Issue will be devoted to collecting contributions aimed at finding a collective approach to the aforementioned challenges. It welcomes papers dealing with concrete financial problems from different perspectives. Contributions related to, for example,  the theory of SPDEs, stochastic mean field games, neural networks solutions, and combinations of these will constitute the core of the present Special Issue, yet not exhausting the set of possible mathematical techniques and/or specific financial models to be analyzed, with special attention paid to those derived from real-world scenarios (e.g., the prediction of production/consumption in energy markets, interest rates structuring, clustering and optimization in productive processes, the quest for effective numerical schemes for SPDEs-based stock-option dynamics, etc.).

Dr. Luca Di Persio
Dr. Francesco Giuseppe Cordoni
Dr. Immacolata Oliva
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. Risks 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 1800 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

  • financial markets
  • stochastic processes in finance
  • SPDEs theory and its applications in finance
  • neural networks for finance
  • stochastic mean field games in finance

Published Papers (3 papers)

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Research

19 pages, 762 KiB  
Article
Calibrating FBSDEs Driven Models in Finance via NNs
by Luca Di Persio, Emanuele Lavagnoli and Marco Patacca
Risks 2022, 10(12), 227; https://doi.org/10.3390/risks10120227 - 30 Nov 2022
Viewed by 1516
Abstract
The curse of dimensionality problem refers to a set of troubles arising when dealing with huge amount of data as happens, e.g., applying standard numerical methods to solve partial differential equations related to financial modeling. To overcome the latter issue, we propose a [...] Read more.
The curse of dimensionality problem refers to a set of troubles arising when dealing with huge amount of data as happens, e.g., applying standard numerical methods to solve partial differential equations related to financial modeling. To overcome the latter issue, we propose a Deep Learning approach to efficiently approximate nonlinear functions characterizing financial models in a high dimension. In particular, we consider solving the Black–Scholes–Barenblatt non-linear stochastic differential equation via a forward-backward neural network, also calibrating the related stochastic volatility model when dealing with European options. The obtained results exhibit accurate approximations of the implied volatility surface. Specifically, our method seems to significantly reduce the neural network’s training time and the approximation error on the test set. Full article
(This article belongs to the Special Issue New Challenges in Mathematical Finance: From S(P)DEs to Machine Learning)
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17 pages, 453 KiB  
Article
Pricing and Hedging Bond Power Exchange Options in a Stochastic String Term-Structure Model
by Lloyd P. Blenman, Alberto Bueno-Guerrero and Steven P. Clark
Risks 2022, 10(10), 188; https://doi.org/10.3390/risks10100188 - 27 Sep 2022
Cited by 2 | Viewed by 1443
Abstract
We study power exchange options written on zero-coupon bonds under a stochastic string term-structure framework. Closed-form expressions for pricing and hedging bond power exchange options are obtained and, as particular cases, the corresponding expressions for call power options and constant underlying elasticity in [...] Read more.
We study power exchange options written on zero-coupon bonds under a stochastic string term-structure framework. Closed-form expressions for pricing and hedging bond power exchange options are obtained and, as particular cases, the corresponding expressions for call power options and constant underlying elasticity in strikes (CUES) options. Sufficient conditions for the equivalence of the European and the American versions of bond power exchange options are provided and the put-call parity relation for European bond power exchange options is established. Finally, we consider several applications of our results including duration and convexity measures for bond power exchange options, pricing extendable/accelerable maturity zero-coupon bonds, options to price a zero-coupon bond off of a shifted term-structure, and options on interest rates and rate spreads. In particular, we show that standard formulas for interest rate caplets and floorlets in a LIBOR market model can be obtained as special cases of bond power exchange options under a stochastic string term-structure model. Full article
(This article belongs to the Special Issue New Challenges in Mathematical Finance: From S(P)DEs to Machine Learning)
31 pages, 526 KiB  
Article
A Bank Salvage Model by Impulse Stochastic Controls
by Francesco Giuseppe Cordoni, Luca Di Persio and Yilun Jiang
Risks 2020, 8(2), 60; https://doi.org/10.3390/risks8020060 - 04 Jun 2020
Cited by 1 | Viewed by 2446
Abstract
The present paper is devoted to the study of a bank salvage model with a finite time horizon that is subjected to stochastic impulse controls. In our model, the bank’s default time is a completely inaccessible random quantity generating its own filtration, then [...] Read more.
The present paper is devoted to the study of a bank salvage model with a finite time horizon that is subjected to stochastic impulse controls. In our model, the bank’s default time is a completely inaccessible random quantity generating its own filtration, then reflecting the unpredictability of the event itself. In this framework the main goal is to minimize the total cost of the central controller, which can inject capitals to save the bank from default. We address the latter task, showing that the corresponding quasi-variational inequality (QVI) admits a unique viscosity solution—Lipschitz continuous in space and Hölder continuous in time. Furthermore, under mild assumptions on the dynamics the smooth-fit W l o c ( 1 , 2 ) , p property is achieved for any 1 < p < + ∞ . Full article
(This article belongs to the Special Issue New Challenges in Mathematical Finance: From S(P)DEs to Machine Learning)
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