Approximation and calibration of laws of solutions to stochastic differential equations | Vidéo | Carmin.tv

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Approximation and calibration of laws of solutions to stochastic differential equations

By Jocelyne Bion-Nadal

Appears in collection : Innovative Research in Mathematical Finance / Recherche innovante en mathématiques financières

In many situations where stochastic modeling is used, one desires to choose the coefficients 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 coefficients 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.

Information about the video

Date of recording 04/09/2018
Date of publication 18/09/2018
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19442903
Cite this video Bion-Nadal, Jocelyne (04/09/2018). Approximation and calibration of laws of solutions to stochastic differential equations. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19442903
URL https://dx.doi.org/10.24350/CIRM.V.19442903

Domain(s)

Probability

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