# Eduardo Abi Jaber

### New

Equilibrium in Functional Stochastic Games with Mean-Field Interaction, with Eyal Neuman and Moritz Voss.

Reconciling rough volatility with jumps, with Nathan De Carvalho.

### Upcoming presentations

# Information

I am currently Assistant Professor (Tenure Track) in Applied Mathematics at Ecole Polytechnique in the Mathematical Finance group of the CMAP department.

I co-organize the Bachelier Seminar and I am responsible of the 3rd-year engineering cycle internships in Mathematical Finance at Ecole Polytechnique.

Research interests: Mathematical finance, stochastic processes, machine learning, volatility modeling, Volterra processes and their applications.

Teaching: Fractional and Volterra processes in Finance (M2 Probabilité et Finance, Ecole Polytechnique-Sorbonne Université) and Deep Learning in Finance (MsC Data cience in Finance, Ecole Polytechnique-HEC).

Mail: eduardo.abi-jaber@polytechnique.edu

Prior to this:

2019-2022: Assistant Professor (Maître de Conférences) in Applied Mathematics at Université Paris 1 Panthéon-Sorbonne, in the CES (Centre d'Economie de la Sorbonne) department.

2021-2022: Associate Researcher in the Mathematical Finance group of the CMAP at Ecole Polytechnique.

2019-2022: Director of Studies of the Master 2 IRFA (Ingénierie du Risque : Finance et Assurance).

2018-2019: Postdoc under the supervision of Prof. Mathieu Rosenbaum at Ecole Polytechnique (DIM Math Innov funding).

2016-2018: PhD under the supervision of Prof. Bruno Bouchard and Prof. Jean-David Fermanian - CIFRE funding from AXA-IM, with supervisor Dr. Camille Illand.

# Awards & grants

AMIES PhD Award, best PhD in collaboration with industry, 2019.

Bachelier Finance Society Junior Scholar Award, most outstanding paper, 2018.

DIM Math Innov, Postdoctoral Fellowship, 2018.

# Publications

[19] Equilibrium in Functional Stochastic Games with Mean-Field Interaction, with Eyal Neuman and Moritz Voss, 2023.

[18] Reconciling rough volatility with jumps, with Nathan De Carvalho, 2023.

[17] The quintic Ornstein-Uhlenbeck volatility model that jointly calibrates SPX & VIX smiles, with Camille Illand and Shaun Li, Risk Magazine (Cutting Edge section), 2023. (iPython notebook)

[16] Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints, with Camille Illand and Shaun Li, 2022.

[15] Optimal Liquidation with Signals: the General Propagator Case, with Eyal Neuman, 2022. (iPython notebook)

[14] Gaussian Agency problems with memory and Linear Contracts, with Stéphane Villeneuve, 2022.

[13] The characteristic function of Gaussian stochastic volatility models: an analytic expression, Finance & Stochastics, 26, 733–769, 2022.

[12] Markowitz portfolio selection for multivariate affine and quadratic Volterra models, with Enzo Miller and Huyên Pham, SIAM Journal on Financial Mathematics, 12(1), 369-409, 2021. (iPython notebook).

[11] Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels, Bernoulli, 27(3), 1583-1615, 2021.

[10] The Laplace transform of the integrated Volterra Wishart process, Mathematical Finance, 32(1), 309-348, 2022.

[9] Integral operator Riccati equations arising in stochastic Volterra control problems, with Enzo Miller and Huyên Pham, SIAM Journal on Control and Optimization, 59(2), 1581-1603, 2021.

[8] Linear-Quadratic control for a class of stochastic Volterra equations: solvability and approximation, with Enzo Miller and Huyên Pham, Annals of Applied Probability, 31(5), 2244-2274, 2021.

[7] A weak solution theory for stochastic Volterra equations of convolution type, with Christa Cuchiero, Martin Larsson and Sergio Pulido, Annals of Applied Probability, 31(6), 2924-2952, 2021.

[6] Lifting the Heston model, Quantitative Finance, 1-19, 2019.

[5] Markovian structure of the Volterra Heston model, with Omar El Euch, Statistics & Probability Letters, Volume 149, Pages 63-72, 2019.

[4] Multifactor approximation of rough volatility models, with Omar El Euch, SIAM Journal on Financial Mathematics, 10(2), 309-349, 2019. (BFS Junior Scholar Award for 'most outsanding paper')

[3] Affine Volterra processes, with Martin Larsson and Sergio Pulido, Annals of Applied Probability, Volume 29, Number 5, 3155-3200, 2019.

[2] Stochastic invariance of closed sets for jump-diffusions with non-Lipschitz coefficients, Electronic Communications in Probability, 22, paper no. 53, 15 pp, 2017.

[1] Stochastic invariance of closed sets with non-Lipschitz coefficients, with Bruno Bouchard and Camille Illand, Stochastic Processes and their Applications, Volume 129, Issue 5, Pages 1726-1748, 2019.

### Thesis

Stochastic invariance and stochastic Volterra equations, PhD thesis, 2018.

# PhD Students

Yuyang Zhao, co-supervised with Mathieu Rosenbaum, 2023 -

Louis-Amand Gérard, co-supervised with Olivier Guéant (Cifre funding GEFIP) 2022-

Nathan De Carvalho, co-supervised with Huyên Pham (Cifre funding ENGIE) 2021-

Shaun Li, co-supervised with Bernard de Meyer (Cifre funding AXA-IM), 2021-

# Talks

### Lectures

Stochastic Methods in Finance and Physics, Creta, Greece, 17-21 July 2023. Minicourse on Volterra processes in Finance. (Invited)

Stochastic Numerics and Statistical Learning: Theory and Applications Workshop, KAUST University, Saudi Arabia, May 28-31, 2023. Mini-course on 'Non-Markovian models in Finance' with Christian Bayer. (Invited)

### Conferences

Advances in Stochastic Analysis for Handling Risks in Finance and Insurance, CIRM Luminy, France, September 11-15, 2023. Equilibrium in Functional Stochastic Games with Mean-Field Interaction (Invited)

Workshop on rough volatility, Isle of Skye, Scotland, May 22-26, 2023. Rough volatility, too smooth? (Invited)

Control & Optimisation Pisa 2023, Pisa, Italy, May 8-10, 2023. A direct approach to a class of finite-players and mean-field games. (Invited)

Workshop Stochastic Control and Risk, Hammamet, Tunisia, April 24-27, 2023. A direct approach to a class of finite-players and mean-field games. (Invited)

London-Paris Bachelier Workshop on Mathematical Finance, Paris, France, September 15-16, 2022, Gaussian Principal-Agent problems with memory. (Invited)

Modeling of Markets with Complex and Rough Regimes, Online, August 31, 2022. Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation. (Invited)

General AMaMeF Conference, 10th Edition, Online, June 22-25, 2021. Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation. (Invited)

Stochastic Analysis and Hermite Sobolev Spaces Workshop, Online, June 21-26, 2021. Linear-quadratic control of stochastic Volterra equations. (Invited)

ILB Rising Talents in Finance and Insurance, Online, March 26, 2021. The characteristic function of Gaussian stochastic volatility models. (Invited)

QuantMinds International, Online, November 2-6, 2020. Reconciling rough volatility with jumps. (Invited)

Advances in Financial Mathematics, Paris, France, January 14-17, 2020. A weak solution theory for stochastic Volterra equations. (Invited)

Journées du Centre d'Economie de la Sorbonne, Université Paris 1, Paris, France, November 14, 2019. Rough volatility modeling and stochastic Volterra equations. (Invited)

Advances in Stochastic Analysis for Handling Risks in Finance and Insurance, CIRM, Luminy, France, October 21-25, 2019. Reconciling rough volatility with jumps. (Invited)

Forum emploi maths, Paris, France, Otcober 15, 2019. The modeling puzzle in the presence of randomness. (AMIES Prize presentation)

Vienna Congress on Mathematical Finance, Vienna, Austria, September 9-13, 2019. Reconciling hyper-rough volatility with jumps.

General AMaMeF Conference, 9th Edition, Paris, France, June 11-14, 2019. Quadratic Volterra processes and multivariate rough volatility modeling. (Invited)

Non linear methods for risk management, Paris, France, October 9, 2018. Lifting the Heston model. (Invited)

Workshop on Finance, Insurance, Probability and Statistics, London, England, September 10-11, 2018. Lifting the Heston model (poster).

European Summer School in Financial Mathematics, 11th Edition, Palaiseau, France, August 27-31, 2018. Lifting the Heston model.

Bachelier Finance Society, 10th world congress, Dublin, Ireland, July 16-20, 2018. Markovian structure of the Volterra Heston model.

IWAP, 9th International Workshop on Applied Probability, Budapest, Hungary, June 18-21, 2018. The Volterra square-root process: Markovian structure and approximation.

Workshop "Long-range fractional processes in Finance", Ecole Polytechnique, Palaiseau, France, June 11, 2018. Lifting the Heston model. (Invited)

Workshop "Robust Finance", Freiburg, Germany, May 16-18, 2018. Lifting the Heston model. (Invited)

Berlin-Paris Young researchers Workshop, 2nd Edition, Stochastic Analysis with applications in Biology and Finance, Paris, France, May 2-4, 2018. Affine Volterra processes. (Invited)

German Probability and Statistics Days 2018, 13th Edition, Freiburg, Germany, February 27 - March 2, 2018. Affine Volterra processes.

Workshop on Quantitative Finance, XIX Edition, Roma, Italy, January 24-26, 2018. Affine Volterra processes.

Bachelier Colloquium, Twelfth Colloquium on Mathematical Finance and Stochastic Calculus, Métabief, France, January 15-20, 2018. Affine Volterra processes.

International Conference on Computational Finance, 2nd Edition, Lisbon, Portugal, September 4 - 8, 2017. Stochastic invariance and applications. (Invited)

European Summer School in Financial Mathematics, 10th Edition, Dresden, Germany, August 28 - September 1, 2017. Affine Volterra processes.

Stochastic Processes and their Applications, 39th Conference, Moscow, Russia, July 24-28, 2017. Stochastic invariance and applications.

General AMaMeF Conference, 8th Edition, Amsterdam, Netherlands, June 19-23, 2017. Stochastic invariance and applications.

Workshop on Quantitative Finance, XVIII Edition, Milano, Italy, January 25-27, 2017. Stochastic invariance of closed sets with non-Lipschitz coefficients. [slides]

Market Microstructure Confronting Many viewpoints, #4, Paris, France, December 6-9, 2016, Stochastic invariance of closed sets with non-Lipschitz coefficients. [slides]

Berlin-Paris Young Researchers Workshop, Stochastic Analysis with applications in Biology and Finance, Berlin, Germany, November 2-4, 2016. Stochastic invariance of closed sets with non-Lipschitz coefficients. [poster]

London-Paris Bachelier Workshop on Mathematical Finance, Paris, France, September 29-30, 2016. Stochastic invariance of closed sets with non-Lipschitz coefficients. [poster]

### Seminars

Groupe de Travail Mathématiques financières et probabilités, LPSM, November 23, 2023. From the Quintic OU model that jointly calibrates SPX-VIX smiles to signature volatility models.

Séminaire de Probabilités, Ecole Polytechnique, October 24, 2023.

Seminar of the Department of Economics and Finance, Luiss University, Rome, September 21, 2023. Equilibrium in Functional Stochastic Games with Mean-Field Interaction.

Seminar on Finance & Modeling, Université Paris 1, France, April 17, 2023. The Quintic model that jointly calibrates SPX/VIX.

Finance and Stochastics seminar, Imperial College, London, England, March 28, 2023. From the Quintic model that jointly calibrates SPX/VIX to Sig-Volatility models.

Séminaire FDD-FIME, Institut Henri Poincaré, December 16, 2022, Optimal execution with transient impact and signals.

STAR seminar, University of Oslo, Online, May 6, 2022. Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation.

Talks in Financial and Insurance Mathematics, ETH-Zürich, Switzerland, April 28, 2022. Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation.

Séminaire Bachelier, January 14, 2021, Deep pricing with quantization hints.

Osaka Webinar on Mathematical Finance, Online, November 25, 2021, Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation.

Berlin Probability Colloquium of the International Research Training Group (IRTG), June 2, 2021, Stochastic Volterra equations : theory, numerics and control.

Séminaire Bachelier, February 4, 2021, Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation.

Groupe de Travail: Finance mathématique, probabilités numériques et statistique des processus, Université Paris Diderot, January 21, 2021, Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation.

Groupe de Travail Probabilités et Mathématiques financières, Université d'Evry, Evry, France, November 12, 2020. Linear-quadratic control of stochastic Volterra equations.

Séminaire du SAMM, Université Paris 1, Paris, France, October 23, 2020. Linear-quadratic control of stochastic Volterra equations.

Finance and Stochastics seminar, Imperial College, London, England, March 11, 2020. Linear-quadratic control of stochastic Volterra equations.

Risk & Stochastics and Financial Mathematics Seminar, London School of Economics, London, England, March 12, 2020. Reconciling rough volatility with jumps.

Vienna Seminar in Mathematical Finance and Probability, Vienna University, Austria, January 30, 2020. Linear-quadratic control of stochastic Volterra equations.

Séminaire Bachelier, Paris, France, December 13, 2019. Linear-quadratic control of stochastic Volterra equations.

Talks in Financial and Insurance Mathematics, ETH-Zürich, Switzerland, October 29, 2019. Linear quadratic control of stochastic Volterra equations.

Seminar on Finance & Modeling, Université Paris 1, France, October 16, 2019. Invariance and viability: from finite dimensional ODEs to infinite dimensional SDEs.

Séminaire du SAMM, Université Paris 1, Paris, France, October 11, 2019. Stochastic Volterra equations.

Groupe de Travail Méthodes Stochastiques et Finance, Ecole des Ponts, INRIA & Université Paris Est, Noisy, France, April 18, 2019. Affine and quadratic Volterra processes and applications.

Matinée scientifique du Ceremade, Université Dauphine, Paris, France, January 15, 2019. Stochastic Volterra equations.

Stochastic Analysis and Stochastics of Financial Markets, Humboldt/TU Universities, Berlin, Germany, November 8, 2018. Lifting the Heston model.

Groupe de Travail Probabilités et Mathématiques financières, Université d'Evry, Evry, France, February 1, 2018. Affine Volterra processes.

Groupe de Travail Méthodes Stochastiques et Finance, Ecole des Ponts, INRIA & Université Paris Est, Noisy, France, October 19, 2017. Affine Volterra processes.

Post/Doctoral Seminar in Mathematical Finance, ETH-Zürich, Switzerland, October 10, 2017. The Volterra square-root process.

Séminaires de l’équipe de Probabilités et Statistiques, Université Paris 13, Paris, France, May 17, 2017. Stochastic invariance and applications. [slides]

Séminaire des Jeunes Chercheurs du Ceremade, Université Paris Dauphine, Paris, France, February 23, 2017, Invariance of closed sets, from regular ODEs to irregular SDEs. [slides]

PhD Students' Day - CEREMADE, Université Paris Dauphine, Paris, France, October 20, 2016. Invariance of closed sets, an intuitive overview. [slides]

Groupe de Travail Méthodes Stochastiques et Finance, Ecole des Ponts, INRIA & Université Paris Est, Noisy, France, October 13, 2016. Stochastic invariance of closed sets with non-Lipschitz coefficients. [slides]

# Teaching

## Ongoing at Ecole Polytechnique

Fractional and Volterra processes in Finance, M2 Probabilité et Finance, X-Sorbonne Université (15h)

Deep Learning in Finance, MsC Data Science in Finance X-HEC (24h).

## Previous

### Lectures

2021-2022 at ENSAE: Numerical Methods in Financial Engineering (3A, 12h), Introduction to mathematical finance (2A, 18h)

2019-2022 at Université Paris 1 Panthéon-Sorbonne: Market Risk Measures (M2, 18h), Calibration in Quantitative Finance (M2, 18h), Topics in Machine Learning (M2, 18h).

### Tutorial classes

2022 at Ecole Polytechnique : Markov chains and martingales (MAP432, 20h)

2019-2022 at Université Paris 1 Panthéon-Sorbonne: Mathematics of insurance and risks (M2, 16h), Mathematical finance (M1, 24h), Integration and Probability (L3, 42h), Analysis (L3, 42h), Linear Algebra (L2, 30h).

2016-2018 at Université Paris Dauphine: Jump processes, Valuation and No Arbitrage (M2 MASEF).