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evenements:seminaireproba-math-fi [2019/01/07 09:29]
Valérie Picot
evenements:seminaireproba-math-fi [2019/03/19 13:03] (current)
Valérie Picot
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 **__Exposés de l'​année 2019__ :** **__Exposés de l'​année 2019__ :**
 +
 +**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
 +++
 +
 +**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..
 +++
 +
 +**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..
 +++
  
 **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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