Français
Approximation and calibration of laws of solutions to stochastic differential equations
Post-edited
Authors : Bion-Nadal, Jocelyne (Author of the conference)
CIRM (Publisher )
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
CIRM (Publisher )
Abstract :
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
Keywords : stochatic differential equation; Wasserstein distance
MSC Codes : 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
Keywords : stochatic differential equation; Wasserstein distance
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
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 18/09/2018 Conference Date : 04/09/2018 Subseries : Research talks arXiv category : Probability Mathematical Area(s) : Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:29:37 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-09-04_Bion_Nadal.mp4 
|
Information on the Event
Event Title : Innovative Research in Mathematical Finance / Recherche innovante en mathématiques financièresEvent Organizers : Callegaro, Giorgia ; Jeanblanc, Monique ; Lépinette, Emmanuel ; Molchanov, Ilya ; Schweizer, Martin ; Touzi, Nizar Dates : 03/09/2018 - 07/09/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1816.html
Citation Data
DOI : 10.24350/CIRM.V.19442903Cite 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 |
See Also
- [Multi angle] Set-valued risk measures of non-convex portfolios / Author of the conference Molchanov, Ilya.
- [Multi angle] Discounting invariant FTAP for large financial markets / Author of the conference Balint, Daniel.
- [Multi angle] From multivariate quantiles to set-valued risk measures: a set optimization - approach to financial models with frictions / Author of the conference Hamel, Andreas H..
- [Multi angle] Pricing without martingale measure / Author of the conference Carassus, Laurence.
Bibliography
- C. Aliprantis and K. Border, Infinite Dimensional Analysis, 1999. - http://dx.doi.org/10.1007/3-540-29587-9
- J. Claisse, D. Talay, and X. Tan, A Pseudo-Markov Property for Controlled Diffusion Processes, SIAM Journal on Control and Optimization, vol.54, issue.2, pp.1017-1029, 2016. - https://dx.doi.org/10.1137/151004252
- W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, 1975. - https://dx.doi.org/10.1007/978-1-4612-6380-7
- W. H. Fleming and M. Soner, Controlled Markov Processes and Viscosity Solutions, of Stochastic Modelling and Applied Probability, 2006. - https://doi.org/10.1007/978-3-662-03961-8
- A. Friedman, Partial Differential Equations of Parabolic Type, 1964. - https://doi.org/10.1007/978-1-4612-0949-2
- J. Hiriart-urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms I. Grundlehren der mathematische Wissenschaften, 1993. - https://dx.doi.org/10.1007/978-3-662-02796-7
- I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, vol.113, 1991. - https://dx.doi.org/10.1007/978-1-4612-0949-2
- N. V. Krylov, Nonlinear Elliptic and Parabolic Equations of the Second Order, 1987 - https://dx.doi.org/10.1007/978-94-010-9557-0
- H. Kunita, Stochastic differential equations and stochastic flows of diffeomorphisms. ´ Ecole d'´ eté de probabilités de Saint-Flour, p.1982, 1984. - https://dx.doi.org/10.1007/978-4-431-68532-6_13
- A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, of Progress in Nonlinear Differential Equations and their Applications, 1995. - https://dx.doi.org/10.1007/978-3-0348-0557-5
- D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, Fundamental Principles of Mathematical Sciences Series, 1999. - https://dx.doi.org/10.1007/978-3-662-06400-9
- D. W. Stroock and S. R. Varadhan, Multidimensional Diffusion Processes, Fundamental Principles of Mathematical Sciences, 1979. - https://dx.doi.org/10.1007/3-540-28999-2
