Encadrement de thèse
- Thèse de Kaouther Hajji, université Paris 13, "Accélaration de la méthode de Monte Carlo
pour des processus de diffusions et applications en finance", soutenue le 12 décembre 2014.
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Thèse de Thi Bao Tram NGO, université Paris 13, Théorèmes limites pour la méthode
MLMC pour plusieurs modèles : processus exponentiel Lévy, EDS dirigée par un processus
de Lévy à sauts purs et processus de diffusion avec une approximation antithétique",
soutenue le 09/07/2021.
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Thèse de Houssem DAHBI, en cotutelle entre l'université de Rouen et l'université de Sousse (Tunisie),
"Parametric estimation for a class of
multidimensional affine processes", soutenue le 13/12/2024, co-encadrant Hamdi Fathallah.
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Thèse de Djibril SARR, thèse CIFRE, université de Paris 13,
"Stochastic Financial Modeling and Machine Learning
for Risk-Neutral and Real-World Market Indicators,
Model Calibration and Data Quality", soutenue le 29/11/2024, en co-direction avec Ahmed Kebaier.
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Thèse de Syrine Hemdène, université de Rouen,
"Inférence de modèles de type affine avec changement de régime", depuis 01/10/2024.
Prépublications
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Truncated sequential guaranteed estimation for the Cox-Ingersoll-Ross models. En collaboration avec Serge Pergamenchtchikov et Thi Bao Tram Ngo, Soumis (2025). https://arxiv.org/abs/2504.04923.
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Ergodicity and Law-of-large numbers for the Volterra Cox-Ingersoll-Ross process.
En collaboration avec Martin Friesen et Jonas Kremer, Soumis (2024). https://arxiv.org/abs/2409.04496.
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Asymptotic properties of AD(1, n) model and its maximum likelihood estimator. En collaboration avec Houssem Dahbi et Hamdi Fathallah Soumis (2023). https://arxiv. org/abs/2303.08467.
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Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process.
En collaboration avec Martin Friesen et Jonas Kremer, Soumis (2024). https://arxiv.org/abs/2404.05554.
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Asymptotic properties and drift parameter estimations of the ergodic double Heston model based on continuous-time observations.
En collaboration avec Houssem Dahbi et Hamdi Fathallah, Soumis 2024, https://arxiv.org/abs/2501.17100.
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On Conditional least squares estimation for the AD(1,n) model.
En collaboration avec Houssem Dahbi et Hamdi Fathallah, https://arxiv.org/abs/2406.07653.
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Financial Stochastic Models Diffusion: From Risk-Neutral to Real-World Measure.
En collaboration avec Ahmed Kebaier et Djibril Sarr, soumis 2024, https://arxiv.org/abs/2409.12783.
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Credit Spreads' Term Structure: Stochastic Modeling with CIR++ Intensity.
En collaboration avec Ahmed Kebaier et Djibril Sarr , Soumis 2024, https://arxiv.org/abs/2409.09179.
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Deep Calibration of Interest Rates Model.
En collaboration avec Ahmed Kebaier et Djibril Sarr, Soumis 2023,
https://arxiv.org/abs/2110.15133.
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Mathematical analysis of a delayed SEIRDS epidemics models: deterministic and stochastic approach.
En collaboration avec Walid Ben Aribi et Slimane Ben Miled {\em Soumis} (2022). \url{https://arxiv.org/abs/2208.07690}.
Publications
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Ben Alaya, M., Pergamenchtchikov, S et Ngo, T.B.T. :
Optimal guaranteed estimation methods for the Cox -Ingersoll -Ross models.
Accepté à Stochastics.
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Ben Alaya, M., Kebaier, A. et Ngo, T.B.T. :
Asymptotic behavior of the multilevel type error for SDEs driven by a pure jump Lévy process.
Accepté à Theory of Probability and its Applications.
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Ben Alaya, M., Kebaier, A., Pap, G., et Tran, N.K.
Local asymptotic properties for the growth rate of a jump-type CIR process.
Accepté à Stochastic Processes and their Applications.
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Ben Alaya, M. Kaouther Hajji, K. et Ahmed Kebaier, A. : Improved adaptive Multilevel Monte Carlo and applications to finance. Stochastics. 95(2), 303-327, (2023).
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Ben Alaya, M. Kebaier, A & Ngo, T. B. T. : Central Limit Theorem for the antithetic multilevel Monte Carlo method.
Annals of Applied Probability. 32, no. 3, 1970-2027, (2022).
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Ben Alaya, M. Kebaier, A &Tran, N. K. :
Local asymptotic properties for Cox-Ingersoll-Ross process with discrete observations. Scandinavian Journal of Statistics. 47, no. 4, 1401-1464, (2020).
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Ammar, H, Ben Alaya, M. & Ben Aribi, W :
Stochastic global optimization using tangent minorants for Lipschitz functions. Journal of Computational and Applied Mathematics. 373 (2020).
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Barczy, M. Ben Alaya, M. Kebaier, A. & Pap, G: Asymptotic properties of maximum likelihood estimator for the growth rate for a stable CIR process based on continuous time observations. Statistics. 53, no. 3, (2019).
- Barczy, M. Ben Alaya, M. Kebaier, A. & Pap, G: Maximum likelihood estimators for a jump-type Heston model.
Journal of Statistical Planning and Inference, 198, 139-164, (2019).
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Barczy, M. Ben Alaya, M. Kebaier, A. & Pap, G: Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations.
Stochastic Processes and their Applications, 128, no. 4, 1135-1164, (2018).
- Ben Alaya, M. Hajji K. & Kebaier, A:
Importance Sampling and Statistical Romberg method for Lévy Processes.
Stochastic Processes
and their Applications, 126, no. 7, 1901-1931, (2016).
, (2016).
- Ben Alaya, M. Hajji K. & Kebaier, A:
Importance Sampling and Statistical Romberg method. Bernoulli Journal
, 21, no. 4, 1947-1983, (2015).
- Ben Alaya, M & Kebaier, A: Central Limit Theorem for the Multilevel Monte Carlo Euler Method.
Annals of Applied Probability. 25(1), 211-234, (2015).
- Ben Alaya, M & Kebaier, A: Multilevel Monte Carlo for Asian options and limit theorems. Monte Carlo Methods and Applications. 20(3), 181-194, (2014).
- Ben Alaya, M & Kebaier, A: Asymptotic Behavior of the Maximum Likelihood Estimator for Ergodic and Nonergodic
Square-Root Diffusions. Stochastic Analysis and Applications. 31(4), 552-573, (2013).
- Ben Alaya, M & Kebaier, A: Parameter estimation for the square root diffusions: ergodic and nonergodic cases.
Stochastic Models. 28(4), 609-634, (2012).
- Ben Alaya, M & Huillet, T & Porzio, A : On an extension of min-semistable distributions.
Probab. Math. Statist.
27(2), 303-323, (2007).
- Ben Alaya, M & Jourdain, B : Probabilistic approximation of a nonlinear parabolic equation
occuring in rheology. Journal of Applied Probability
44(2), 528-546, (2007).
- Ben Alaya, M & Huillet, T : On a functional equation genelatizing the class of semistable
distributions.
Annals of the Institute of Statistical Mathematics,
57(4), 817-831, (2005).
- Ben Alaya, M & Huillet, T : On max-multiscaling distributions as extended max-semistable
ones. Stochastic Models,
20(4), 493-512, (2004).
- Ben Alaya, M & Huillet, T : On Lévy-Fréchet processes and related self-similar and semistable ones.
Chaos, Solitons and Fractals,
14(5), 57-76, (2002).
- Ben Alaya, M & Huillet, T & Porzio, A : On Lévy stable and semistable distributions.
Fractals,
9(3), 347-364, (2001).
- Ben Alaya, M & Huillet, T & Porzio, A : On the physical relevance of max- and log-max-selfsimilar distributions.
Eur. Phys. J. B.,
17, 147-158, (2000).
- Ben Alaya, M & Gilles Pagès : Rate of convergence for computing expectations of stopping functionals
of an $\alpha-$mixing process . Advances in Applied Probability,
30, 425-448(1998).
- Ben Alaya, M : Résolution des équations elliptiques par la méthode du shift.
Mathematics and computers in simulation, 38, 87--96(1995).
- Ben Alaya, M : On the simulation of random variables depending on a stopping time.
Stochastic Analysis and Applications,
11(2), 133-153(1993).
- Ben Alaya, M : Sur la méthode du shift en simulation.
N. Bouleau et D. Talay, eds, Probabilités Numériques,
volume 10, chapitre 2, pages 61-66, INRIA, (1992).
.
Le mémoire de mon HDR est disponible ici.