A Message from the outgoing President

A very warm welcome to the first BFS Newsletter in 2026!

I end my tenure as the BFS President just as I started it: with preparations for the BFS World Congress, as this biennial event marks milestones for the society. Back in 2024, we met in Rio de Janeiro, our first ever congress in South America. It was a fantastic event, and I remain ever so grateful to the local organising team at the FGV for their incredible effort. I am confident 2026 will see a repeat of this success. We might in fact hold our largest ever BFS World Congress and I hope to see you all in Bologna, 29 June to 3 July: submissions are still open!

But BFS is about much more than just the biennial congress and many things happen behind the scenes. One of the first working groups I set up updated our Mission and Vision statements. BFS “is an international organization dedicated to advancing research and its applications in the broad field of mathematical finance. We foster and connect the diverse international community of academic researchers and industry practitioners.” As parts of such efforts, I am proud to say we have joined forces with SIAM and in March 2025 we established joint SIAM-BFS Mathematical Finance Online Seminar. This is flagship monthly seminar open to all across the globe. The two societies also jointly support the Financial Mathematics & Engineering Mentoring Program which (re)launched in November 2025.

BFS also “recognizes excellence through prizes and promotes young talents.” In 2025, part of a larger committee restructure, we established a new Prizes Committee, which is busy reviewing existing awards and looking into new ones. The flagship annual Bruti-Liberati Prize for the best doctoral thesis in Mathematical Finance continues and this year’s submissions are open till 30th of January. I am also very happy to announce that the Susquehanna-BFS Junior Scholar Award will continue for at least 6 more years, or 3 more world congress editions. Application for the 2026 Congress are made within the paper submission system. Finally, I am very excited to say that a new Early Career Researcher Travel Award will be announced soon. This initiative will support travel of young researchers in mathematical finance to academic events across the globe, throughout the year. Please check our pages for the announcements and guidelines for organisers on how to seek support.

BFS is dedicated to “advancing the field of mathematical finance through innovative research addressing global challenges and opportunities.” It has been very encouraging to see, over the last two years, a post-pandemic return of a vibrant event schedule in our field. Against the backdrop of often polarised and divided reality, it is uplifting to see an energetic global research community working together across the globe. And times feel ripe for us to be busy, as changes fuelled by AI-technological advances ripple through all sectors, including financial industry. The necessity for mathematically sound understanding of how to deploy such tools and risk-manage their use underscores the pressing need for our research field and offers an opportunity to grow. And many other arising challenges, from climate change, through population demographics, to crypto currencies all call for new mathematical models.

Mathematical finance has always been a broad field, but its scope has expanded markedly in recent years. The diversity of problems we engage with continues to grow, driven both by evolving market structures – such as decentralised finance and new fintech products – and by advances in scientific methodology, including the use of large language models, machine learning tools for synthetic market data generation, or issues of algorithmic collusion. These developments reinforce the need for genuinely interdisciplinary research, with particularly strong links to computer science. At the same time, they cast new light on long-standing questions in mathematical finance, many of which merit renewed attention. The interaction of optimal investment, stochastic control, and reinforcement learning illustrates how classical theory and modern tools can productively interact. These are, in my view, exciting times for our community. I am confident we will embrace new opportunities, questions, and collaborators, while remaining true to our core principles and our commitment to mathematics and rigorous scientific reasoning.

It has been a real honour to serve as your president over the last two years. I am immensely thankful to all colleagues who worked with me in the BFS structures, and to our wider community for your support. I look forward to remaining actively engaged with BFS as your past-president. For now, please join me in offering our wholehearted welcome to our new president, Huyên Pham.

Jan Obloj

BOOK REVIEW

Gaussian Process Models for Quantitative Finance

by Michael Ludkovski and Jimmy Risk

reviewed by Renyuan Xu (Stanford University)

I read this book with great interest and found it useful and inspiring. The book presents Gaussian process (GP) methodology in a technically careful manner while keeping the exposition closely tied to quantitative finance. The material is organized around a set of recurring financial tasks (including derivative pricing, term-structure estimation, and optimal stopping/stochastic control), through which the authors motivate modeling choices, approximation strategies, and computational workflows. This application-driven organization helps clarify what is being approximated, which sources of uncertainty are being modeled, and how these elements interact with the numerical methods used in practice.

A notable aspect of the presentation is its explicit placement of GP methods within a broader methodological landscape. GPs have been developed in parallel across several communities, including machine learning (e.g., Bayesian optimization), applied statistics (kriging and its role in spatial statistics and Bayesian regression), and applied probability (the theory of Gaussian stochastic processes). Because each community uses its own terminology, the literature can be hard to navigate for newcomers. The book’s presentation synthesizes key strands of this literature across communities.

The connection between GPs and machine learning is framed in a genuinely two-way direction. On one hand, the book discusses how neural networks and deep learning tools can be used to approximate GP kernels. On the other hand, it highlights an important complementarity: many ML methods are typically deployed with abundant data, whereas GP modeling provides a flexible, uncertainty-aware framework that can be particularly appropriate in small-data settings. In finance, where data can be limited, nonstationary, or expensive to obtain for certain products and states, this perspective helps motivate why the GP framework is highly relevant.

One stimulating thread in the book that I would like to point out is the use of GP surrogates for stochastic control. The surrogate viewpoint offers an alternative angle on sequential decision problems that relates naturally to reinforcement learning (RL) without relying primarily on PDE-based parameterizations (e.g., directly approximating objects derived from HJB equations). In this framework, GP surrogates serve as probabilistic function approximators that support decision-making under uncertainty, and they provide a bridge to value-based and policy-based reasoning in RL. This interpretation can broaden the set of conceptual and computational tools available for financial decision problems, particularly when model specification is uncertain and direct PDE solutions are impractical.

Overall, the book offers a very nice guide to using GP methodology for inference and decision problems in quantitative finance, with sustained attention to cross-disciplinary connections and a reader-friendly exposition.