## Financial and Actuarial Mathematics, Numerical Probability

#### Day, hour and place

Thursday at 11:00, Jussieu, Salle Paul Lévy, 16-26 209 / Sophie Germain salle 1016

#### Contact(s)

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### Previous talks

#### Year 2024

Financial and Actuarial Mathematics, Numerical Probability

Thursday March 28, 2024, 9AM, Jussieu, Salle Paul Lévy, 16-26 209

**Matinée Anr Reliscope** *To be announced.*

Financial and Actuarial Mathematics, Numerical Probability

Thursday March 21, 2024, 11AM, Sophie Germain salle 1016

**Athena Picarelli** (Université de Verone) *A deep solver for BSDEs with jumps*

Financial and Actuarial Mathematics, Numerical Probability

Thursday March 14, 2024, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**Sergio Pulido** (ENSIIE, Univ. Paris Saclay) *Polynomial Volterra processes*

Financial and Actuarial Mathematics, Numerical Probability

Thursday March 7, 2024, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**Cyril Benezet** (ENSIIE, Univ. Paris Saclay) *Hedging Valuation Adjustment et Risque de Modèle*

Financial and Actuarial Mathematics, Numerical Probability

Thursday February 29, 2024, 10AM, CREDIT AGRICOLE, Pl. des États Unis, Montrouge

**Vincent Lemaire Et Huyên Pham** (LPSM) *Séance Chaire CACIB*

10h accueil

10h30-11h15 Vincent Lemaire (Sorbonne Université / LPSM), Denoising Diffusion Probabilistic Models, introduction et quelques résultats théoriques.

Résumé : Introduits récemment, les modèles génératifs basés sur une dynamique de bruitage/débruitage des données se révèlent très performants. On exposera le cadre mathématique à temps continu qui se base sur les équations différentielles stochastiques et le score matching. On donnera quelques résultats théoriques de convergence et on s'intéressera au comportement de la borne de l'erreur en fonction de la façon dont on bruite (noise schedule). Ce dernier point est un travail en commun avec Claire Boyer, Sylvain Le Corff, Antonio Ocello et Stanislas Strasman.

11h15-11h45 pause café

11h45-12h30 Huyen Pham (Université Paris Cité / LPSM), Nonparametric generative modeling for time series via Schrödinger bridge.

Résumé: We propose a novel generative model for time series based on Schrödinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We estimate the drift function from data samples by nonparametric, e.g. kernel regression methods, and the simulation of the SB diffusion yields new synthetic data samples of the time series.The performance of our generative model is evaluated through a series of numerical experiments. First, we test with autoregressive models, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal, temporal dependencies metrics, and predictive scores. Next, we use our SB generated synthetic samples for the application to deep hedging on real-data sets.

Financial and Actuarial Mathematics, Numerical Probability

Thursday February 8, 2024, 11AM, Sophie Germain salle 1013

**Yadh Hafsi** (Univ. Paris Saclay) *Uncovering Market Disorder and Liquidity Trends Detection*

Financial and Actuarial Mathematics, Numerical Probability

Thursday January 25, 2024, 11AM, Sophie Germain salle 1013

**Fanny Cartelier** (ENSAE) *Can investors curb greenwashing*

Financial and Actuarial Mathematics, Numerical Probability

Thursday January 18, 2024, 11AM, Sophie Germain salle 1016

**Ioannis Gasteratos** (Imperial College London) *Transportation-cost inequalities for nonlinear Gaussian functionals*

Financial and Actuarial Mathematics, Numerical Probability

Thursday January 11, 2024, 11AM, Sophie Germain salle 1016

**Olivier Guéant** (Paris 1) *Incorporating Variable Liquidity in Optimal Market Making and Inventory Management Models: A Comparison of Hawkes Processes and Markov-Modulated Poisson Processes*

#### Year 2023

Financial and Actuarial Mathematics, Numerical Probability

Thursday December 14, 2023, 11AM, Sophie Germain salle 1016

**Camilo Garcia Trillos** (University College London) *Adversarial Distributional Robustness from Wasserstein Ascent-Descent Particle Dynamics*

Financial and Actuarial Mathematics, Numerical Probability

Thursday December 7, 2023, 11AM, Sophie Germain salle 1016

**Caroline Hillairet** (ENSAE) *Bi-Revealed Utilities in a defaultable universe*

the possibility of the default, thus τ adds an additional source of risk. The defaultable universe is represented by the filtration G up to time τ (τ included), where G stands for the progressive enlargement of F by τ . The basic assumption in force is that τ avoids F-stopping times. The bi-revealed problem consists in recovering a consistent dynamic utility from the observable characteristic of an agent. The general results on bi-revealed utilities, first given in a general and abstract framework, are translated in the defaultable G-universe and then are interpreted in the F-universe. The decomposition of G-adapted processes XG provides an interpretation of a G-characteristic XτG stopped at τ as a reserve process. Thanks to the characterization of G-martingales stopped at τ in terms of F-martingales, we establish a correspondence between G-bi-revealed utilities from characteristic and F-bi-revealed pair of utilities from characteristic and reserves. In a financial framework, characteristic can be interpreted as wealth and reserves as consumption. This result sheds a new light on the consumption in utility criterion: the consumption process can be interpreted as a certain quantity of wealth, or reserves, that are accumulated for the financing of losses at the default time.

This is a joint work with N. El Karoui and M. Mrad.

Financial and Actuarial Mathematics, Numerical Probability

Thursday November 30, 2023, 11AM, Sophie Germain salle 1016

**Grégoire Loeper** (BNP Parisba) *Black and Scholes, Legendre and Sinkhorn*

Financial and Actuarial Mathematics, Numerical Probability

Thursday November 23, 2023, 11AM, Sophie Germain salle 1016

**Eduardo Abi Jaber** (CMAP) *From the Quintic model that jointly calibrates SPX/VIX to Signature Volatility models*

For pricing SPX products, we show that the Quintic model is part of a larger class of stochastic volatility model where the volatility is driven by a linear function of the path signature of a Brownian motion enhanced with the running time. For this larger class of models, we develop pricing and hedging methodologies using Fourier inversion techniques on the characteristic function which is known up to an infinite-dimensional Riccati equation. We illustrate our method on numerical examples for pricing, hedging and calibration of vanilla and path-dependent options in several classes of Markovian and Non-Markovian models.

Financial and Actuarial Mathematics, Numerical Probability

Thursday November 16, 2023, 11AM, Sophie Germain salle 1013

**Samuel Daudin** (Univ. Nice) *On the optimal rate for the convergence problem in mean-field control*

Financial and Actuarial Mathematics, Numerical Probability

Thursday October 19, 2023, 11AM, INRIA 2 Rue Simone Iff, 75012 Paris, France

**Robert Denkert** (HU Berlin) *xtended Mean Field Control Problems with Singular Controls*

Financial and Actuarial Mathematics, Numerical Probability

Thursday October 19, 2023, 9AM, Inria 2 Rue Simone Iff, 75012 Paris, France

**Gudmund Pammer** (ETH, Zurich) *Stretched Brownian Motion: Analysis of a Fixed-Point Scheme*

Financial and Actuarial Mathematics, Numerical Probability

Thursday October 19, 2023, 11:45AM, Inria 2 Rue Simone Iff, 75012 Paris, France

**Aurélien Alfonsi** (ENPC) *Nonnegativity preserving convolution kernels. Application to Stochastic Volterra Equations in closed convex domains and their approximation.*

Financial and Actuarial Mathematics, Numerical Probability

Thursday October 19, 2023, 9:45AM, Inria 2 Rue Simone Iff, 75012 Paris, France

**Mehdi Talbi** (LPSM) *Sannikov’s contracting problem with many Agents*

Financial and Actuarial Mathematics, Numerical Probability

Thursday October 12, 2023, 11AM, Sophie Germain salle 1016

**Céline Labart** (Université de Savoie) *To be announced.*

Financial and Actuarial Mathematics, Numerical Probability

Wednesday July 12, 2023, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**Mortiz Voss** (UCLA) *On Adaptive Robust Optimal Execution and Machine Learning Surrogates*

Financial and Actuarial Mathematics, Numerical Probability

Thursday June 15, 2023, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**Thomas Kruse** (Bergischen Universität Wuppertal) *Multilevel Picard approximations for high-dimensional semilinear parabolic PDEs and further applications*

Financial and Actuarial Mathematics, Numerical Probability

Thursday May 11, 2023, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**Botao Li** (LPSM) *Simplified Models and Optimization Algorithms in Deep Learning*

Financial and Actuarial Mathematics, Numerical Probability

Thursday April 13, 2023, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**Xavier Erny** (CMAP) *Propagation du chaos conditionnelle de modèles en champ moyen*

Financial and Actuarial Mathematics, Numerical Probability

Thursday April 13, 2023, 10AM, Jussieu, Salle Paul Lévy, 16-26 209

**Pierre Lavigne** (Institut Louis Bachelier) *Decarbonization of financial markets: a mean field game approach*

We formalize the problem in the setting of mean-field games and prove the existence and uniqueness of a Nash equilibrium for firms. We then present a convergent numerical algorithm for computing this equilibrium and illustrate the impact of climate transition risk and the presence of green-minded investors on the market decarbonization dynamics and share prices.

We show that uncertainty about future climate risks and policies leads to higher overall emissions and higher spreads between share prices of green and brown companies. This effect is partially reversed in the presence of environmentally concerned investors, whose impact on the cost of capital spurs companies to reduce emissions.

Joint work with Peter Tankov.

Financial and Actuarial Mathematics, Numerical Probability

Thursday April 6, 2023, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**Mahmoud Khabou** (INSA Toulouse) *The normal approximation of compound Hawkes functionals*

Financial and Actuarial Mathematics, Numerical Probability

Thursday April 6, 2023, 10AM, Jussieu, Salle Paul Lévy, 16-26 209

**Ziad Kobeissi** (INRIA ILB) *Temporal Difference Learning with Continuous Time and State in the Stochastic Setting*

Financial and Actuarial Mathematics, Numerical Probability

Thursday March 30, 2023, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**Mehdi Talbi** (ETH Zurich) *Mean field games of stopping times*

Financial and Actuarial Mathematics, Numerical Probability

Thursday March 16, 2023, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**Rudy Morel** (Ecole Normale Supérieure) *A statistical model of financial time-series through Scattering Spectra*

These spectra are an extension of the standard wavelet spectrum and are defined as the diagonal of a certain non-linear correlation matrix on wavelet coefficients.

They characterize a wide range of non-Gaussian properties of multi-scale processes. This is analyzed for a variety of processes in the Finance literature.

We prove that self-similar processes have scattering spectra which are scale invariant. This property can be tested statistically on a single realization and defines a class of wide-sense self-similar processes.

We build maximum entropy models conditioned by scattering spectra coefficients, and generate new time-series with a microcanonical sampling algorithm.

Besides capturing statistical properties of observed time-series, these models can be used to predict future volatility and are shown to capture non-trivial statistical properties of the option smile.

Financial and Actuarial Mathematics, Numerical Probability

Thursday March 9, 2023, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**Ofelia Bonesini** (Imperial College) *Correlated equilibria for mean field games with progressive strategies*

Financial and Actuarial Mathematics, Numerical Probability

Thursday February 16, 2023, 11AM, Jussieu, Salle Paul Lévy, 16-26 209

**William Hammersley** (Univ. Nice) *A prospective regularising common noise for mean field systems*

Financial and Actuarial Mathematics, Numerical Probability

Thursday February 2, 2023, 4PM, Jussieu, Salle Paul Lévy, 16-26 209

**Nabil Kazi-Tani** (Université de Lorraine) *The role of correlation in diffusion control ranking games*

Financial and Actuarial Mathematics, Numerical Probability

Thursday January 26, 2023, 4:30PM, Jussieu, Salle Paul Lévy, 16-26 209

**Manal Jakani** (Le Mans Université) *Approximation of reflected SDEs in time-dependent domains and applications to Generalized BSDEs and PDE in time-dependent domain*

Financial and Actuarial Mathematics, Numerical Probability

Thursday January 19, 2023, 4:30PM, Jussieu, Salle Paul Lévy, 16-26 209

**Andrea Mazzon** (LMU München) *Detecting asset price bubbles using deep learning*

Financial and Actuarial Mathematics, Numerical Probability

Thursday January 5, 2023, 4PM, Jussieu, Salle Paul Lévy, 16-26 209

**Ahmed Kebaier** (Université d'Evry) *The interpolated drift implicit Euler scheme Multilevel Monte Carlo method for pricing Barrier options and applications to the CIR and CEV models*

Financial and Actuarial Mathematics, Numerical Probability

Thursday January 5, 2023, 5PM, Jussieu, Salle Paul Lévy, 16-26 209

**Thomas Wagenhofer** (TU Berlin) *Weak error estimates for rough volatility models*

Our main result is that moments of these integrals have a weak error rate of order 3H+1/2 if H<1/6 and order 1 otherwise. For this we first derive a moment formula for both the discretization and the true stochastic integral. We then use this formula and properties of Gaussian random variables to prove our main theorems. Furthermore, we show that this convergence rate also holds for slightly more general payoffs and also provide a lower bound. Note that our rate of 3H+1/2 is in stark contrast to the strong error rate which is of order H.

#### Year 2022

Financial and Actuarial Mathematics, Numerical Probability

Thursday December 15, 2022, 4PM, Jussieu, Salle Paul Lévy, 16-26 209

**Nizar Touzi** (CMAP, Ecole Polytechnique) *Arrêt optimal en champ moyen*

Financial and Actuarial Mathematics, Numerical Probability

Thursday December 15, 2022, 5PM, Jussieu, Salle Paul Lévy, 16-26 209

**Olivier Bokanowski** (Univ. Paris Cité, LJLL) *Neural Networks for First Order HJB Equations*

Financial and Actuarial Mathematics, Numerical Probability

Thursday November 24, 2022, 4:30PM, Jussieu, Salle Paul Lévy, 16-26 209

**Pierre Bras** (LPSM, Sorbonne Université) *Total variation convergence of the Euler-Maruyama scheme in small time with unbounded drift*

Financial and Actuarial Mathematics, Numerical Probability

Thursday October 20, 2022, 4PM, Jussieu, Salle Paul Lévy, 16-26 209

**Damien Lamberton** (Université Gustave Eiffel) *Régularité de la frontière libre d'un problème d'arrêt optimal : une approche probabiliste*

Financial and Actuarial Mathematics, Numerical Probability

Thursday October 20, 2022, 5PM, Jussieu, Salle Paul Lévy, 16-26 209

**Aurélien Alfonsi** (Ecole des Ponts) *Approximation of Stochastic Volterra Equations with kernels of completely monotone type (Joint work with Ahmed Kebaier)*

Financial and Actuarial Mathematics, Numerical Probability

Thursday October 6, 2022, 4:30PM, Jussieu, Salle Paul Lévy, 16-26 209

**Michaël Allouche** (Ecole Polytechnique) *Estimation of extreme quantiles from heavy-tailed distributions with neural networks*

Financial and Actuarial Mathematics, Numerical Probability

Thursday July 7, 2022, 4PM, Sophie Germain salle 1016

**Anthony Reveillac** (INSA Toulouse) *Malliavin calculus for Hawkes functionals and application to Insurance*

Financial and Actuarial Mathematics, Numerical Probability

Thursday June 23, 2022, 5PM, Sophie Germain salle 1016

**Boualem Djehiche** (KTH Stockholm) *On zero-sum Dynkin games of mean field type.*

This is a joint work with Roxana Dumistrescu.

Financial and Actuarial Mathematics, Numerical Probability

Thursday June 2, 2022, 5PM, Jussieu, Salle Paul Lévy, 16-26 209 / Sophie Germain salle 1016

**Marcos Lopes De Prado** (ADIA) *Open problems in Finance*

Financial and Actuarial Mathematics, Numerical Probability

Thursday May 12, 2022, 5PM, Sophie Germain salle 1016

**Maximilien Germain** (Université Paris Cité, LPSM) *A level-set approach to the control of state-constrained McKean-Vlasov equations: application to portfolio selection*

Financial and Actuarial Mathematics, Numerical Probability

Thursday April 28, 2022, 4PM, Sophie Germain salle 1016

**Nabil Khazi-Tani** (IECL, université de Lorraine) *To be announced.*

Financial and Actuarial Mathematics, Numerical Probability

Thursday March 17, 2022, 4PM, Sophie Germain salle 1016

**Pierre Cardaliaguet** (Ceremade, Université Paris-Dauphine) *On the convergence rate for the optimal control of McKean-Vlasov dynamics*

Financial and Actuarial Mathematics, Numerical Probability

Thursday March 17, 2022, 5PM, Sophie Germain salle 1016

**Haoyang Cao** (École Polytechnique) *Identifiability in Inverse Reinforcement Learning*

Financial and Actuarial Mathematics, Numerical Probability

Thursday March 3, 2022, 5PM, Sophie Germain salle 1016

**Jodi Dianetti** (Bielefeld University) *Submodular mean field games: Existence and approximation of solutions*

Financial and Actuarial Mathematics, Numerical Probability

Thursday February 17, 2022, 4PM, Sophie Germain salle 1016

**David Métivier** (CMAP, Ecole Polytechnique) *Interpretable hidden Markov model for stochastic weather generation and climate change analysis*

Financial and Actuarial Mathematics, Numerical Probability

Thursday February 17, 2022, 5PM, Sophie Germain salle 1016

**Sergio Pulido** (LaMME, ENSIEE) *The rough Heston model with self-exciting jumps*

Financial and Actuarial Mathematics, Numerical Probability

Thursday February 3, 2022, 4PM, Jussieu, Salle Paul Lévy, 16-26 209

**Peter Tankov** (CREST, ENSAE) *Optimal Exploration of an Exhaustible Resource with Stochastic Discoveries*

` reserves as well as a finite unexplored area available for exploration with constant marginal cost, resulting in a Poisson process of new discoveries. We prove that a frontier of critical levels of ``proven`

reserves exists, above which exploration is stopped, and below which it happens at infinite speed. This frontier is increasing in the explored area, and higher ``proven'' reserve levels along this critical threshold are indicative of more scarcity, not less. In our stochastic generalization of Hotelling's rule, price expectations conditional on the current state rise at the rate of interest across exploratory episodes. However, the state-dependent conditional expected path of prices realized prior to exhaustion of the exploratory area rises at a rate lower than the rate of interest, consistent with most empirical tests based on observed price histories.
Financial and Actuarial Mathematics, Numerical Probability

Thursday February 3, 2022, 5PM, Jussieu, Salle Paul Lévy, 16-26 209

**Alexandre Pannier** (Imperial College, Londres) *Rough multi-factor volatility models for SPX and VIX*

Financial and Actuarial Mathematics, Numerical Probability

Thursday January 20, 2022, 5PM, Jussieu, Salle Paul Lévy, 16-26 209

**Philippe Bergault** (Ecole Polytechnique) *A mean field game of market making against strategic traders*