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evenements:seminaireproba-math-fi [2019/01/07 09:29]
Valérie Picot
evenements:seminaireproba-math-fi [2019/05/03 11:37] (current)
Valérie Picot
Line 7: Line 7:
  
 **__Exposés de l'​année 2019__ :** **__Exposés de l'​année 2019__ :**
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 +**16 mai à 14h00 :** <color #088A85> Aurélien ​ Alfonsi </​color> ​ (  Ecole des Ponts ParisTech) ​ //   ​Approximation of OT problems with marginal moments contraints (Joint work with Rafaëll Coyaud, Virginie Ehrlacher and Damiano Lombardi)//
 +++ Voir résumé |  \\Optimal Transport (OT) problems arise in a wide range of applications,​ from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the relaxation of the OT problem when the marginal constraints are replaced by some moment constraints. Using Tchakaloff'​s theorem, we show that the Moment Constrained Optimal Transport problem (MCOT) is achieved by a finite discrete measure. Interestingly,​ for multimarginal OT problems, the number of points weighted by this measure scales linearly with the number of marginal laws, which is encouraging to bypass the curse of dimension. This approximation method is also relevant for Martingale OT problems. We show the convergence of the MCOT problem toward the corresponding OT problem. In some fundamental cases, we obtain rates of convergence in $O(1/n)$ or $O(1/n^2)$ where $n$ is the number of moments, which illustrates the role of the moment functions. Last, we present algorithms exploiting that the MCOT is reached by a finite discrete measure and provide numerical examples of approximations..
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 +**18 avril à 14h00 :** <color #088A85> Roxana Dumitrescu </​color> ​ (King'​s College London) ​ //  Mean-field games of optimal stopping: a relaxed solution approach//
 +++ Voir résumé |  \\We consider the mean-field game where each agent determines the optimal time to exit the game by solving anoptimal stopping problem with reward function depending on the density of the state processes of agents still present in thegame. We place ourselves in the framework of relaxed optimal stopping, which amounts to looking for the optimal occupationmeasure of the stopper rather than the optimal stopping time. This framework allows us to prove the existence of the relaxedNash equilibrium and the uniqueness of the associated value of the representative agent under mild assumptions. Further, weprove a rigorous relation between relaxed Nash equilibria and the notion of mixed solutions introduced in earlier works on thesubject, and provide a criterion, under which the optimal strategies are pure strategies, that is, behave in a similar way tostopping times. Finally, we present a numerical method for computing the equilibrium in the case of potential games and showits convergence (joint work with  Peter Tankov and G. Bouveret).
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 +**11 avril à 14h00 :** <color #088A85> Caroline Hillairet </​color> ​ (ENSAE) //  Aggregation of  heterogeneous ​ consistent progressive utilities//
 +++ Voir résumé |  \\We aim  to describe globally the behavior and preferences of heterogeneous agents. Our starting point is the aggregate wealth of a given economy, with a given repartition of the wealth among investors, which is not necessarily Pareto optimal. We propose a construction of an aggregate forward utility, market consistent,​that aggregates the marginal utility of the heterogeneous agents. This construction is based on the aggregation of the pricing kernels of each investor. As an application we analyze the impact of the heterogeneity and of the wealth market on the yield curve.
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 +Joint work with Nicole El Karoui et Mohamed Mrad.
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 +**4 avril à 14h00 :** <color #088A85> Xiaolu Tan </​color> ​ (Université Paris-Dauphine) //  From Martingale Optimal Transport to McKean-Vlasov Control Problems//
 +++ Voir résumé |  \\The Martingale Optimal Transport (MOT) problem consists in maximizing a reward value among a class of martingales with given marginal distributions. It is motivated by its application in finance to obtain the no-arbitrage price bounds of derivative options in a data calibrated market. We consider a class of MOT problems and show how it could be related to a McKean-Vlasov (mean-field) control problem, which is a large population control problem. We then study the dynamic programming principle and the numerical approximation of the McKean-Vlasov control problem.
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 +**4 avril à 15h00 :** <color #088A85> Ahmed Kebaier </​color> ​ (Université Paris 13) // Non-asymptotic error bounds for The Multilevel Monte Carlo Euler method applied to SDEs with constant diffusion coefficient//​
 +++ Voir résumé |  \\In this work, we are interested in deriving non-asymptotic error bounds for the multilevel Monte Carlo method. As a first step, we deal with the explicit Euler discretization of stochastic differential equations with a constant diffusion coefficient. We prove that, as long as the deviation is below an explicit threshold, a Gaussian-type concentration inequality optimal in terms of the variance holds for the multilevel estimator. To do so, we use the Clark-Ocone representation formula and derive bounds for the moment generating functions of the squared difference between a crude Euler scheme and a finer one and of the squared difference of their Malliavin derivatives.
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 +**28 mars à 14h00 :** <color #088A85> Carl Graham </​color> ​ (Ecole Polytechnique) //  Théorèmes limites pour un processus de Hawkes avec auto excitation et inhibition à portée bornée//
 +++ Voir résumé |  \\Les processus de Hawkes avec une fonction de reproduction pouvant prendre des valeurs positives et négatives permettent de modéliser des propriétés d’auto-excitation et d’auto-inhibition de leurs points. Le cas d’une fonction de reproduction positive correspond à de l'​auto-excitation pure et est bien compris. Elle admet en particulier une représentation en tant que processus de branchement avec immigration qui permet d’appliquer des résultats sur les arbres de Galton-Watson. Nous utilisons des techniques de renouvellement pour obtenir des théorèmes limites dans le cas de fonctions de reproduction à support borné pouvant prendre des valeurs négatives. Nous avons en particulier obtenu des inégalités de concentration exponentielles. Une étape importante de la preuve a été de montrer l’existence de moments exponentiels pour les durées de renouvellement de files d’attente de type M/G/infini apparaissant naturellement dans ce cadre, ce qui est en soi un résultat général intéressant.
 +
 +Travail en collaboration avec Manon Costa, Viet Chi Tran et Laurence Marsalle
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 +**22 fevrier à 14h00 :** <color #088A85> Eva Löcherbach</​color> ​ (Université Paris 1) //  Oscillations pour des systèmes de processus de Hawkes en interactions//​
 +++ Voir résumé |  \\On considère un système de processus de Hawkes non-linéaires avec des interactions en champ moyen pour modéliser des séquences de trains de décharge dé neurones. Après avoir étudié la limite de grande population d’un tel système (autrement dit, la propriété de propagation de chaos), j’expliquerai comment les non-linéarités dans la dynamique limite engendrent du comportement périodique et donc des oscillations auto-entretenues du système. Ceci est un travail commun avec Susanne Ditlevsen..
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 +
 +**14 fevrier à 14h00 :** <color #088A85> Tahir Chouilli</​color> ​ (University of Alberta) //  Deflators and log-optimal portfolios for markets under random horizon//
 +++ Voir résumé |  \\The goal of this talk is to ``measure''​ the impact ​ of a random horizon on log-optimal portfolios. This random horizon is a general random time that might represent the default time of a firm, the death time of an insured, or more generally an occurrence time of an even that might impact the market somehow. Herein, in this setting, we address the num\'​eraire portfolio and  the log-utility maximization problem. Due to the duality between the investment strategies and the deflators, our ultimate goal translates to the description of the impact of the random horizon on the optimal deflator. Thus, our first principal result lies in explicitly describing the set of all deflators for a model stopped at a random time in different manners. ​ Once the set of all deflators is completely and explicitly parametrized,​ we address the minimization problem over the set of these deflator. For the case of log utility, this optimal deflator is completely and explicitly described in different manners using the flow information generated by the initial market model only. As a result, we conclude that the random horizon leads naturally to an implied random utility. ​ Concerning the num\'​eraire portfolio, we establish a one-to-one connection between the num\'​eraire portfolio for models stopped at the random time  and  the num\'​eraire portfolio for models under ``public''​ information only. This talk is based on joint works with Sina Yansori (University of Alberta).
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 +
 +**7 fevrier à 14h00 :** <color #088A85> Yann Braouezec</​color> ​ (IESEG School of Management) // Stress testing banks’ balance sheets : model and empirical application to the six American systemic banks//
 +++ Voir résumé |  \\We consider a stress test model in which each bank, after an exogenous shock, may have to sell a portion of its assets in order to comply with regulatory constraints. We calibrate our model using the six banks with significant trading operations and we show that, depending on the price impact, the contagion of failures may be significant. Our results may be used to refine current stress testing frameworks by incorporating potential contagion mechanisms between banks..
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 +**31 janvier à 14h00 :** <color #088A85> Simone Scotti</​color> ​ (Paris Diderot) ​ // The Alpha-Heston Stochastic Volatility Model//
 +++ Voir résumé |  \\We introduce an affine extension of the Heston model where the instantaneous variance
 +process contains a jump part driven by alpha-stable processes with alpha in (1,2]. In this framework, we examine the implied volatility and its asymptotic behaviors for both asset and variance options. Furthermore,​ we examine the jump clustering phenomenon observed on the variance market and provide a jump cluster decomposition which allows to analyse the cluster processes..
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 **24 janvier à 14h00 :** <color #088A85> Carlo Sgarra </​color>​ (Politecnico di Milano) // Estimation of a Self-Exciting Jump Diffusion Model for Oil Price by a Particle Markov Chain Monte Carlo Method// **24 janvier à 14h00 :** <color #088A85> Carlo Sgarra </​color>​ (Politecnico di Milano) // Estimation of a Self-Exciting Jump Diffusion Model for Oil Price by a Particle Markov Chain Monte Carlo Method//
 ++ Voir résumé |  \\In this paper we propose a self-exciting jump diffusion model for oil price dynamics based on a Hawkes-type process. In particular, the jump intensity is stochastic and path dependent, implying that a jump will increase the probability of observing a new jump and this feature of the model aims at explaining the jumps clustering effect. These kind of models are now very popular in mathematical finance and financial econometrics,​ but the existing literature is mainly focused on the equity market. In contrast, we fit our model to spot prices related to the WTI crude oil at daily frequency and the estimation is performed by applying a suitable modification of Particle Markov Chain Monte Carlo method proposed by Andrieu \& al. \cite{holestein}. Finally, we provide an in the sample and out of the sample analysis in order to test the validity of our approach. (Paper written in Cooperation with L. Gonzato, Milano Bicocca and ESSEC). ++ Voir résumé |  \\In this paper we propose a self-exciting jump diffusion model for oil price dynamics based on a Hawkes-type process. In particular, the jump intensity is stochastic and path dependent, implying that a jump will increase the probability of observing a new jump and this feature of the model aims at explaining the jumps clustering effect. These kind of models are now very popular in mathematical finance and financial econometrics,​ but the existing literature is mainly focused on the equity market. In contrast, we fit our model to spot prices related to the WTI crude oil at daily frequency and the estimation is performed by applying a suitable modification of Particle Markov Chain Monte Carlo method proposed by Andrieu \& al. \cite{holestein}. Finally, we provide an in the sample and out of the sample analysis in order to test the validity of our approach. (Paper written in Cooperation with L. Gonzato, Milano Bicocca and ESSEC).
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 **__Exposés de l'​année 2018__ :** **__Exposés de l'​année 2018__ :**
  
evenements/seminaireproba-math-fi.1546849742.txt.gz · Last modified: 2019/01/07 09:29 (external edit)

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