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 6085

Special Issue Editors

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
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
Special Issues, Collections and Topics in MDPI journals
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

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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
Risks 2022, 10(12), 227; https://doi.org/10.3390/risks10120227 - 30 Nov 2022
Viewed by 1369
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
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17 pages, 453 KiB  
Article
Pricing and Hedging Bond Power Exchange Options in a Stochastic String Term-Structure Model
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