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Mrad Mohamed

Associate Professor-HDR

HDR entitled ''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 of the Institut Louis Bachelier depuis 2022.

Contact: mrad at math.univ-paris13.fr 

Team Probabilités et Statistiques

Projects

  • Member of the chair  ACTIONS, ”Actuaries for Change in Technologies and Insurees Opportunities for Next Steps” (Février 2024-2028), financed by BNP Paribas Cardif in partnership with Fondation du Risque et l’Institut des Actuaires.

  • Member of the  l'ANR "DREAMES" Numerical Methods for Decision: Dynamic Preferences And Multivariate Risks, October 2021---October 2025.

  • Co-leader of the EIF project, Intergenerational Risk Sharing in Pension Plans.

  • Associate member of the Research Initiative, Risques Emergents ou Atypiques en Assurance (RE2A), MMA-COVEA, IRA, École polytechnique, Fondation du Risque (ILB),  see https://www.idr-re2a.eu

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).                            "Stochastic control and applications: Mean field types and dynamic utilities" defended in October 2022.  

Research Interest

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- Dynamic Utilities:

  • Consistent Dynamic Utilities "forward utilities". 

  • SPDE of HJB type: Resolution using the stochastic characteristics method.

  • Long-Term Yield Curves Modelling,  Ramsey Rule. 

  • Learning Preferences: Revealed Utilities, Application to Robot-Advisors.

- Numerical Methods:​

  • Strong Convergence Rate of Compound Random Maps, Application to SPDE 

  • Memory reduction in simulations: Inversion of schemes and prime number generators.

  • Multi-Level Monte Carlo methods for the compound of two SDEs.

 - Intergenerational risks.

  • Pension funds​

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.

Submitted papers

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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.

Works nearing completion

Contact

  1. E. Gobet, Pierre Cohort and M. Mrad "Approximation Scheme Compounding And Random Number Generator Inversion", 2025.

  2. Mohamed Mrad and Chefia Ziri,  " Deep Learning for Revealed Dynamic Utilities", 2025.

  3. Nicole El Karoui and Mohamed Mrad, "Forward Utility as Backward Value Function",  2025.

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

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

  6. Ahmed Kebaier, Vincent Lemaire and Mohamed Mrad, MLMC for compound random maps, 2024.

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