Lionel Lenôtre
Université de Haute-Alsace (UHA), Haut Rhin, Faculty Member
- INRIA, Nancy Grand-Est, France, Department Memberadd
We consider the skew diffusion processes and their simulation. This study are divided into four parts and concentrate on the processes whose coefficients are piecewise constant with discontinuities along a simple hyperplane. We start by a... more
We consider the skew diffusion processes and their simulation. This study are divided into four parts and concentrate on the processes whose coefficients are piecewise constant with discontinuities along a simple hyperplane. We start by a theoretical study of the one-dimensional case when the coefficients belong to a broader class. We particularly give a result on the structure of the resolvent densities of these processes and obtain a computational method. When it is possible, we perform a Laplace inversion of these densities and provide some transition functions. Then we concentrate on the simulation of skew diffusions process. We build a numerical scheme using the resolvent density for any Feller processes. With this scheme and the resolvent densities computed in the previous part, we obtain a simulation method for the skew diffusion processes in dimension one. After that, we consider the multidimensional case. We provide a theoretical study and compute some functionals of the sk...
Research Interests:
Nous considerons les processus de diffusion biaises et leur simulation. Notre etude se divise en quatre parties et se concentre majoritairement sur les processus a coefficients constants par morceaux dont les discontinuites se trouvent le... more
Nous considerons les processus de diffusion biaises et leur simulation. Notre etude se divise en quatre parties et se concentre majoritairement sur les processus a coefficients constants par morceaux dont les discontinuites se trouvent le long d'un hyperplan simple. Nous commencons par une etude theorique dans le cas de la dimension un pour une classe de coefficients plus large. Nous donnons en particulier un resultat sur la structure des densites des resolvantes associees a ces processus et obtenons ainsi une methode de calcul. Lorsque cela est possible, nous effectuons une inversion de Laplace de ces densites et donnons quelques fonctions de transition. Nous nous concentrons ensuite sur la simulation des processus de diffusions baisees. Nous construisons un schema numerique utilisant la densite de la resolvante pour tout processus de Feller. Avec ce schema et les densites calculees dans la premiere partie, nous obtenons une methode de simulation des processus de diffusions bia...
Research Interests:
The study of skew diffusion is of primary concern for their implication in the mod-eling and simulation of diffusion phenomenons in media with interfaces. First, we provide results on one-dimensional processes with discontinuous... more
The study of skew diffusion is of primary concern for their implication in the mod-eling and simulation of diffusion phenomenons in media with interfaces. First, we provide results on one-dimensional processes with discontinuous coefficients and their connections with the Feller theory of generators as well as the oneof stochastic differential equations involving local time. Second, in view of developing new simulation techniques, we give a method to compute the density and the resolvent kernel of skew diffusions which can be extended to Feller processes in general. Explicit closed-form are given for some particular cases.
Research Interests:
Research Interests:
This paper reviews different statistical methods dedicated to the post-processing of Numerical Weather Predictions and Ensemble Forecast. We focus on the application of the post-processing to problems linked to the production of... more
This paper reviews different statistical methods dedicated to the post-processing of Numerical Weather Predictions and Ensemble Forecast. We focus on the application of the post-processing to problems linked to the production of electricity by eolian devices. The basic idea is to give a concise panorama of the methods commonly used nowadays. We pay a particular attention to the mathematics involved in the methods. We do not compare the methods and do not provide some preferences. Classification. 62-02; 62P12.
Research Interests:
We provide two numerical schemes for the sample paths simulation of skew diffusions with piecewise constant coefficients. Both of these schemes use the resolvent kernel. Precisely, the first scheme use only the resolvent kernel while the... more
We provide two numerical schemes for the sample paths simulation of skew diffusions with piecewise constant coefficients. Both of these schemes use the resolvent kernel. Precisely, the first scheme use only the resolvent kernel while the second use it as less as possible. Moreover, in the second, some sampled positions are exact.
Research Interests:
Research Interests:
Research Interests:
In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and... more
In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distribution. For the pricing and hedging model, we chose a classical Black & choles model with a stochastic interest rate following a Hull & White model. The risk management model describing the evolution of the parameters of the pricing and hedging model is a Gaussian model. The new numerical method is compared with the traditional nested simulation approach. We review the convergence of both methods to estimate the risk indicators under consideration. Finally, we provide numerical results showing that the sparse grid approach is extremely competitive for models with moderate dimension.