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Audiovisual Mathematics Library

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Multi angle

Authors : Imkeller, Peter (Author of the conference)
CIRM (Publisher )

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Abstract : Backward stochastic differential equations have been a very successful and active tool for stochastic finance and insurance for some decades. More generally they serve as a central method in applications of control theory in many areas. We introduce BSDE by looking at a simple utility optimization problem in financial stochastics. We shall derive an important class of BSDE by applying the martingale optimality principle to solve an optimal investment problem for a financial agent whose income is partly affected by market external risk. We then present the basics of existence and uniqueness theory for solutions to BSDE the coefficients of which satisfy global Lipschitz conditions.

MSC Codes :
60H10 - Stochastic ordinary differential equations
60H15 - Stochastic partial differential equations
91B24 - Price theory and market structure
91G80 - Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)

Additional resources :
http://smai.emath.fr/cemracs/cemracs17/Slides/imkeller.pdf

Information on the Video

Film maker :

Hennenfent, Guillaume

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Download :

https://videos.cirm-math.fr/2017-07-17_Imkeller.mp4

Information on the Event

Event Title : CEMRACS - Summer school: Numerical methods for stochastic models: control, uncertainty quantification, mean-field / CEMRACS - École d'été : Méthodes numériques pour équations stochastiques : contrôle, incertitude, champ moyen
Event Organizers : Bouchard, Bruno ; Chassagneux, Jean-François ; Delarue, François ; Gobet, Emmanuel ; Lelong, Jérôme
Dates : 17/07/17 - 25/08/17
Event Year : 2017
Event URL : http://conferences.cirm-math.fr/1556.html

Citation Data

DOI : 10.24350/CIRM.V.19198303
Cite this video as: Imkeller, Peter (2017). An introduction to BSDE. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19198303
URI : http://dx.doi.org/10.24350/CIRM.V.19198303

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Bibliography

El Karoui, N., Peng, S., & Quenez, M.C. (1997). Backward stochastic differential equations in finance. Mathematical Finance, 7(1), 1–71 - http://dx.doi.org/10.1111/1467-9965.00022

Hu, Y., Imkeller, P., & Müller, M. (2005). Utility maximization in incomplete markets. The Annals of Applied Probability, 15(3), 1691-1712 - http://dx.doi.org/10.1214/105051605000000188

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