m
• E

F Nous contacter

0

Post-edited

H 2 Approximation and calibration of laws of solutions to stochastic differential equations

Auteurs : Bion-Nadal, Jocelyne (Auteur de la Conférence)
CIRM (Editeur )

 Loading the player... coupling measure new Wasserstein type distance Hamilton-Jacobi-Bellman equation one dimensional case Hölder regular multidimensional case Kakutani fixed point method approximation by diffusion laws optimal coupling measure

Résumé : In many situations where stochastic modeling is used, one desires to choose the coefficients of a stochastic differential equation which represents the reality as simply as possible. For example one desires to approximate a diffusion model
with high complexity coefficients by a model within a class of simple diffusion models. To achieve this goal, we introduce a new Wasserstein type distance on the set of laws of solutions to d-dimensional stochastic differential equations.
This new distance $\widetilde{W}^{2}$ is defined similarly to the classical Wasserstein distance $\widetilde{W}^{2}$ but the set of couplings is restricted to the set of laws of solutions of 2$d$-dimensional stochastic differential equations. We prove that this new distance $\widetilde{W}^{2}$ metrizes the weak topology. Furthermore this distance $\widetilde{W}^{2}$ is characterized in terms of a stochastic control problem. In the case d = 1 we can construct an explicit solution. The multi-dimensional case, is more tricky and classical results do not apply to solve the HJB equation because of the degeneracy of the differential operator. Nevertheless, we prove that this HJB equation admits a regular solution.

Keywords : stochatic differential equation; Wasserstein distance

Codes MSC :
60H15 - Stochastic partial differential equations
60H30 - Applications of stochastic analysis (to PDE, etc.)
60J60 - Diffusion processes
91B70 - Stochastic models in economics
93E20 - Optimal stochastic control

 Informations sur la Vidéo Langue : Anglais Date de publication : 18/09/2018 Date de captation : 04/09/2018 Collection : Research talks ; Probability and Statistics Format : MP4 (.mp4) - HD Durée : 00:29:37 Domaine : Probability & Statistics Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2018-09-04_Bion_Nadal.mp4 Informations sur la rencontre Nom de la rencontre : Innovative Research in Mathematical Finance / Recherche innovante en mathématiques financièresOrganisateurs de la rencontre : Callegaro, Giorgia ; Jeanblanc, Monique ; Lépinette, Emmanuel ; Molchanov, Ilya ; Schweizer, Martin ; Touzi, NizarDates : 03/09/2018 - 07/09/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1816.html Citation Data DOI : 10.24350/CIRM.V.19442903 Cite this video as: Bion-Nadal, Jocelyne (2018). Approximation and calibration of laws of solutions to stochastic differential equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19442903 URI : http://dx.doi.org/10.24350/CIRM.V.19442903

Voir aussi

Bibliographie

Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée

0
Z