2025 Joint SIAM-BFS Online Seminars
2025
Date: Thursday, 11 December 2025
Speaker: Erhan Bayraktar (University of Michigan)
Title: A Mean-Field Approach to DeFi Currency Exchanges
Abstract: We investigate the behavior of liquidity providers (LPs) by modeling a decentralized cryptocurrency exchange (DEX) based on Uniswap v3. LPs with heterogeneous characteristics choose optimal liquidity positions subject to uncertainty regarding the size of exogenous incoming transactions and the prices of assets in the wider market. They engage in a game among themselves, and the resulting liquidity distribution determines the exchange rate dynamics and potential arbitrage opportunities of the pool. We calibrate the distribution of LP characteristics based on Uniswap data and the equilibrium strategy resulting from this mean-field game produces pool exchange rate dynamics and liquidity evolution consistent with observed pool behavior. We subsequently introduce Maximal Extractable Value bots who perform Just-In-Time liquidity attacks, and develop a Stackelberg game between LPs and bots. This addition results in more accurate simulated pool exchange rate dynamics and stronger predictive power regarding the evolution of the pool liquidity distribution.
Thursday, 11 December 2025, 19:00 (GMT +1)
Link to registration:
https://siam.zoom.us/webinar/register/WN_s8rIcHwiS-uPM3Dkuok-Wg
Date: Thursday, 13 November 2025
Speaker: Luciano Campi (University of Milan)
Title: Optimal coarse correlated equilibria in mean field games
Abstract: We will consider coarse correlated equilibria (CCE) in continuous time mean field games. CCEs are generalizations of Nash equilibria, when a moderator (correlation device) recommend strategies to the players that are not convenient to unilaterally reject. We will first address existence and approximations results when the number of players goes to infinity. Second, we will provide a linear programming approach through the notion of relaxed strategies in the same spirit as the works by Kurtz and Stockbridge, which have been recently extended to mean field games in several papers by Bouveret, Dumitrescu, Leutscher and Tankov. Within such a linear programming setting and under some regularity assumptions, we will show existence of an optimal CCE with respect to a fixed criterion for the moderator. Finally, we will propose an equivalent Lagrangian formulation and a primal-dual algorithm to compute an optimal CCE numerically. This talk is based on joint papers with F. Cannerozzi, F. Cartellier, M. Fischer and I. Tzouanas
Thursday, 13 November 2025, 19:00 (GMT +1)
Link to registration:
https://siam.zoom.us/webinar/register/WN_s8rIcHwiS-uPM3Dkuok-Wg
Date: Thursday, 9 October 2025
Speaker: Nicole Bäuerle (Karlsruher Institut für Technologie (KIT))
Title: Competitive portfolio optimization
Abstract: Within a common arbitrage-free semimartingale financial market we consider the problem of determining all Nash equilibrium investment strategies for n agents who try to maximize the expected utility of their relative wealth. The utility function can be rather general here. Exploiting the linearity of the stochastic integral and making use of the classical pricing theory we are able to express all Nash equilibrium investment strategies in terms of the optimal strategies for the classical one agent expected utility problems. We give applications to specific financial markets and compare our results with those given in the literature. A more specific model with price impacts is also discussed. Moreover, we consider the problem of determining all Nash equilibrium investment strategies for n agents who try to maximize the expected utility of their wealth under the constraint that with certain probability the own wealth exceeds a linear combination of the others. We compare the investment strategy to the optimal one without competition. (Joint work with T. Göll)
Thursday, 9 October 2025, 19:00 (GMT +2)
Link to registration:
https://siam.zoom.us/webinar/register/WN_s8rIcHwiS-uPM3Dkuok-Wg
Date: Thursday, 11 September 2025
Speakers: Chiara Amorino (University of Barcelona) and
Fayçal Drissi (University of Oxford)
Titles: Minimax rate for multivariate data under componentwise local differential privacy constraints (C. Amorino)
Equilibrium Liquidity Provision in Concentrated Liquidity Automated Market Makers (F. Drissi)
Abstracts:
C. Amorino:
Our research analyses the trade-off between maintaining privacy and preserving statistical accuracy when dealing with multivariate data subject to componentwise local differential privacy (CLDP). Under CLDP, each component of the private data is released through a separate privacy channel. This allows for varying levels of privacy protection for different components or for the privatization of each component by different entities, each with their own distinct privacy policies. It also covers practical situations where it is impossible to privatize all components of the raw data jointly.
We develop general techniques for establishing minimax bounds that quantify the statistical cost of privacy as a function of the privacy levels \alpha_1,…,\alpha_d of the d components. The versatility and efficiency of these techniques are demonstrated through various statistical applications. Specifically, we examine nonparametric density estimation and joint moments estimation under CLDP, providing upper and lower bounds that match up to constant factors, along with an associated data-driven adaptive procedure. We also conduct a detailed analysis of the effective privacy level, exploring how information about a private characteristic of an individual may be inferred from the publicly visible characteristics of the same individual.
F. Drissi:
Automated market makers (AMMs) with concentrated liquidity (CL) are the most widely used decentralised exchanges, with daily trading volumes around $4 billion. In CL markets, liquidity providers (LPs) strategically choose price ranges to balance fee revenues against adverse selection losses. We develop a model of competition among LPs and characterise the equilibrium distribution of liquidity across ranges. The analysis shows how equilibrium outcomes depend on the number of competing LPs, the ratio of informed to uninformed trading flow, and wealth heterogeneity among liquidity providers. Finally, we examine the role of “noise” liquidity provision and show how it affects equilibrium allocations and execution costs.
Thursday, 11 September 2025, 19:00 (GMT +2)
Link to registration:
https://siam.zoom.us/webinar/register/WN_s8rIcHwiS-uPM3Dkuok-Wg
Date: Thursday, 12 June 2025
Speakers: Purba Das (King’s College London) and
Valentin Tissot-Daguette (Bloomberg)
Titles: Invariance of Stochastic integral with respect to the choice of partitions (P. Das)
Pathwise Superhedging of Asian Claims (V. Tissot-Daguette)
Abstracts:
P. Das:
We study the concept of quadratic variation of a continuous path along a sequence of partitions and its dependence with respect to the choice of the partition sequence. We introduce the concept of quadratic roughness of a path along a partition sequence and show that for Hölder-continuous paths satisfying this roughness condition, the quadratic variation along balanced partitions is invariant with respect to the choice of the partition sequence. We further present several constructions of paths and processes with finite quadratic variation along a refining sequence of partitions and, in particular, study the dependence of quadratic variation with respect to the sequence of partitions for these constructions.
V. Tissot-Daguette:
The talk unveils pathwise superhedging strategies for convex Asian claims using a dynamic hedge in the underlying and a static position in vanilla options. For an Asian call, where the seller is long the matching vanilla contract, the dynamic hedge may involve the time spent by the asset – or its running average – above the strike. The validity of average-based strategies stems from a mysterious identity relating the Asian call payoff to a strip of binary options across maturities.
The strategies are then tested on synthetic data, where we compare the variance of their P&Ls and hedging turnover. We finally connect these findings with Martingale Optimal Transport and derive robust price bounds for forward start (convex) Asian claims.
Special thanks to Bruno Dupire, Hélyette Geman, Julien Guyon, Bryan Liang, Marcel Nutz, and Nizar Touzi.
Thursday, 12 June 2025, 19:00 (GMT +2)
Link to registration:
https://siam.zoom.us/webinar/register/WN_s8rIcHwiS-uPM3Dkuok-Wg
Date: Thursday, 8 May 2025
Speaker: Julio Backhoff (University of Vienna)
Title: Of ‘most exciting’ games and the specific relative entropy between martingales.
Abstract: The laws of two continuous martingales will typically be singular to each other and hence have infinite relative entropy. But this does not need to happen in discrete time. This suggests defining a new object, the specific relative entropy, as a scaled limit of the relative entropy between the discretized laws of the martingales. This definition goes back to Nina Gantert’s PhD thesis, and in recent time Hans Foellmer has rekindled the study of this object. Independently, this object has made sporadic appearances in finance over the years, for instance in works by Avellaneda et al. and more recently Dolinsky and Cohen.
In this talk we will first discuss the existence of a closed-form formula for the specific relative entropy, depending on the quadratic variation of the involved martingales. Next we will describe an application of this object to prediction markets. Concretely, David Aldous asked in an open question to determine the ‘most exciting’ game, i.e. the prediction market with the highest entropy. With M. Beiglböck we give an answer to this question by solving a stochastic control problem whose cost criterion is the specific relative entropy. Finally we will discuss an application to the ‘most exciting’ game with multiple outcomes, based on joint work with Wang and Zhang, highlighting a novel connection to the field of Monge-Ampere equations.
Thursday, 8 May 2025, 19:00 (GMT +2)
Date: Thursday, 10 April 2025
Speaker: Sara Svaluto-Ferro (University of Verona)
Title: Signature-based models: theory, calibration, and expansions
Abstract: Signature methods provide a non-parametric approach to extracting features from trajectories, offering versatile applications in finance. The structure of signature components enables the use of advanced mathematical tools and the construction of highly general models capable of capturing diverse behaviors.
In this talk, we introduce the concept of the signature and its key properties, illustrating its potential through two financial applications.
The first application focuses on a stochastic volatility model where volatility dynamics are described by linear functions of the (time-extended) signature of a primary process. When this process is of polynomial type, its truncated signature retains this structure, allowing for closed-form expressions of the squared VIX. By incorporating the Brownian motion driving the stock price, both the log-price and the squared VIX can be expressed linearly in terms of the signature of the augmented process, achieving highly accurate calibration results for SPX and VIX options.
The second application examines the local-in-time expansion of a continuous-time process and its conditional moments, including the characteristic function. By leveraging the time-extended Itô signature—composed of iterated integrals of deterministic and stochastic signals (time, multiple correlated Brownian motions, and compound Poisson processes)—we derive automated expansions to any order with explicit coefficients. This provides stochastic representations suitable for asymptotic analysis in the short-time limit.
Thursday, 10 April 2025, 19:00 (GMT +2)
Slides to talk:
slides_svaluto-ferro_250410
Date: Thursday, 20 March 2025
Speakers: Terry Lyons (University of Oxford) and
Luhao Zhang (Johns Hopkins University)
Titles: The Mathematics of Complex Streamed Data (T. Lyons)
A Class of Interpretable and Decomposable Multi-period Convex Risk Measures (L. Zhang)
Abstracts:
T. Lyons:
Multimodal streamed data is essentially different to unimodal streamed data. Consider this:
‘A commuter arrives at a bus stop before the bus’ – they catch it;
‘The bus arrives first’ – they miss it.
These are the same two events, but the order changes everything. Yet most models treat these as identical: ‘A bus and a person arrived’ They ignore timing and relationships.
This simplification isn’t harmless. A timed series gives no information about order within sampling intervals. As a result, the sampling rate has to come from the bottom up if it is to preserve this order information. Rough path theory makes a radical change and describes the stream over an interval using a group element. According to the choice of group it is possible to capture order information and to allow a top down description of the data stream without using essential information about the order of events.
This approach to describing streamed data is important to data science because it reduces the dimension needed for descriptive feature sets and so reduces the size of the data set needed to train. There are numerous prize winning illustrations of the methodology in use and the impact can be measured in the hundreds of millions of US dollars.
L. Zhang:
Multi-period risk measures evaluate the risk of a stochastic process by assigning it a scalar value. A desirable property of these measures is dynamic decomposition, which allows the risk evaluation to be expressed as a dynamic program. However, many widely used risk measures, such as Conditional Value-at-Risk, do not possess this property. In this work, we introduce a novel class of multi-period convex risk measures that do admit dynamic decomposition.
Our proposed risk measure evaluates the worst-case expectation of a random outcome across all possible stochastic processes, penalized by their deviations from a nominal process in terms of both the likelihood ratio and the outcome. We show that this risk measure can be reformulated as a dynamic program, where, at each time period, it assesses the worst-case expectation of future costs, adjusting by reweighting and relocating the conditional nominal distribution. This recursive structure enables more efficient computation and clearer interpretation of risk over multiple periods.
Thursday, 20 March 2025, 18:00 (GMT +1)
Date: Thursday, 23 January 2025
Speaker: Scott Robertson (Boston University)
Title: Rational Expectations Equilibrium with Endogenous Information Acquisition Time
Abstract: In this talk, we establish equilibrium in the presence of heterogeneous information. In particular, there is an insider who receives a private signal, an uninformed agent with no private signal, and a noise trader with semi price-inelastic demand. The novelty is that we allow the insider to decide (optimally) when to acquire the private signal. This endogenizes the entry time and stands in contrast to the existing literature which assumes the signal is received at the beginning of the period. Allowing for optimal entry also enables us to study what happens before the insider enters with private information, and how the possibility for future information acquisition both affects current asset prices and creates demand for information related derivatives. Results are valid in continuous time, when the private signal is a noisy version of the assets’ terminal payoff, and when the quality of the signal depends on the entry time.
Thursday, 23 January 2025, 19:00 (GMT +1)
