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Mrad Mohamed

Maître de Conférences-HDR

HDR intitulée ''Utilités dynamiques et schémas numériques'', soutenue le 28 Janvier 2022. "HDR.pdf"

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Laboratoire Analyse, Géométrie et Applications (LAGA). 

Université  Sorbonne Paris Nord.

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 Academic Fellow de l’Institut Louis Bachelier depuis 2022.

Contact: mrad at math.univ-paris13.fr 

Equipe Probabilités et Statistiques

Projets

  • Membre de l'ANR "DREAMES" Numerical Methods for Decision: Dynamic Preferences And Multivariate Risks, Octobre 2021---Octobre 2025.

  • Co-porteur du projet EIF, Intergenerational Risk Sharing in Pension Plans.

  • Membre associé de l'Initiative de Recherche, Risques Emergents ou Atypiques en Assurance (RE2A), MMA-COVEA, IRA, Ecole polytechnique, Fondation du Risque (ILB),  see https://www.idr-re2a.eu

Current PhD Students

  • Chefia  Ziri (2018-22): PhD at Le Mans University and University Tunis El Manar, supervisor Anis Matoussi, co-supervisors Mohamed Mnif (ENIT-LAMSIN, University Tunis El Manar) and Mohamed Mrad (Université Sorbonne, Paris Nord).                             

  •  Marouen Abdouli (2021-):   PhD at Le Mans University and University Tunis El Manar, supervisor Anis Matoussi, co-supervisors Mohamed Mnif (ENIT-LAMSIN, University Tunis El Manar) and Mohamed Mrad (Université Sorbonne, Paris Nord).

  • Guillaume Broux-Quemerais (2021-), PhD at Le Mans University, supervisors Anis Matoussi and Mohamed Mrad (Université Sorbonne, Paris Nord).

Research Interest

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- Utilités dynamiques:

  • Utilités Dynamiques Consistantes "forward utilities". 

  • EDPS de type HJB. Résolution par la méthode des caractéristiques stochastiques.

  • Courbes de taux Long terme, Règle de Ramsey. 

  • Apprentissage des préférences: utilités révélées.

- Méthodes numériques:

  • Résolution des EDPS par la méthode de caractéristiques stochastiques.

  • Approximation de la composée de champs aléatoires. 

  • Réduction  de mémoire lors de simulations: Inversion des schémas et des générateurs de  Nombres Pseudo-aléatoires.

  • Méthodes de Monte Carlo Multi-Level pour la composée de deux EDSs.

 - Risques Intergénérationnels.

  • Fonds de pensions​

Publications

  1. Nicole El Karoui, Caroline Hillairet and Mohamed Mrad, Bi-revealed utilities in a defaultable universe : a new point of view on consumption.  Probability, Uncertainty and Quantitive Risk (2024), hal-03919186.

  2. Caroline Hillairet, Sarah Kaäkai and Mohamed Mrad, Time-consistent pension policy with minimum guarantee and sustainability constraint.  Probability, Uncertainty and Quantitive Risk (2024), arXiv :2207.01536.

  3. Anis Matoussi and Mohamed Mrad, Dynamic Utility and related nonlinear SPDE driven by Lévy Noise. IJTAF, Vol. 25 No 01,  2250004, 2022.

  4.  Nicole El Karoui, Caroline Hillairet and Mohamed Mrad, Ramsey rule with forward/backward utility for long-term yield curves modeling. Decisions in Economics and Finance, 2022, vol. 45, no 1, p. 375-414.

  5. Mohamed Mrad, Solving some Stochastic Partial Differential Equations driven by Lévy Noise using two SDEs.   ”Stochastics, 2022, p. 1-34”.

  6.   Nicole El Karoui, Mohamed Mrad, Recover Dynamic Utility from Observable Process, Application to the economic equilibrium, SIAM Journal on Financial Mathematics, 2021, vol. 12, no 1, p. 189-225.

  7.   Mohamed Mrad, Random Risk Aversion and Explicit Consistent Utility Construction, International Journal of Theoretical and Applied Finance (IJTAF) Volume 24, Issue 1, 2021.

  8.   Nicole El Karoui, Mohamed Mrad and Caroline Hillairet, Construction of an aggregate consistent utility, without Pareto optimality, In book, Frontiers in Stochastic Analysis - BSDEs, SPDEs and their Applications, Springer 2019.

  9.   Nicole El Karoui, Mohamed Mrad and Caroline Hillairet, Consistent Utility of Invest- ment and Consumption : a Forward/Backward SPDE viewpoint, Stochastics, Vol. 90, No. 6 2018, p. 927-954.

  10.   Emmanuel Gobet and Mohamed Mrad, Convergence Rate Of Strong Approximations Of Compound Random Maps, Discrete & Continuous Dynamical Systems- Series B, 2018, vol 23, no 10.

  11.  Emmanuel Gobet and Mohamed Mrad, Strong approximation of stochastic processes at random times and application to their exact simulation, An International Journal of Probability and Stochastic Processes Volume 89, 2017.

  12.  Nicole El Karoui,  Caroline Hillairet and Mohamed Mrad, Affine Long Term Yield Curves : an application of the Ramsey Rule with Progressive Utility, Journal of Financial Engineering Journal of Financial Engineering, Vol. 1, No. 1 (2014).

  13.  Nicole El Karoui and Mohamed Mrad, An Exact Connection between two Solvable SDEs and a Non Linear Utility Stochastic PDEs, SIAM Journal on Financial Mathematics, Vol. 4, No. 1, 2013 pages 697-736.

Articles soumis

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  1. Mohamed Mrad and Alexandre Popier, Solving some Stochastic Partial Differential Equations driven by non-finite Lévy measue using two SDEs. (2023), hal-04040355.

Travaux en cours de finalisation

Contact

  • E. Gobet, Pierre Cohort and M. Mrad "Approximation Scheme Compounding And Random Number Generator Inversion", (2024)

  • M. Jakani , C. Hillairet and M. Mrad  "Indifference  and Marginal Indifference Pricing Using Consistent Stochastic Utilities", (2024)

  • Nicole El Karoui and Mohamed Mrad, Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows, Preprint (2024). Disponible sur HAL.

  • Ahmed Kebaier, Vincent Lemaire and Mohamed Mrad, MLMC for compound random maps. (2023).

  • Mohamed Mrad, "Indifference Pricing by Consistent Progressive Stochastic Utilities", (2021).

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