Volume 44, Number 5, September-October 2010Special Issue on Probabilistic methods and their applications
|Page(s)||1107 - 1133|
|Published online||26 August 2010|
Probabilistic methods for semilinear partial differential equations. Applications to finance
Department of Mathematics, Imperial College London, 180 Queen's Gate,
London, SW7 2AZ, UK. email@example.com; firstname.lastname@example.org
With the pioneering work of [Pardoux and Peng, Syst. Contr. Lett. 14 (1990) 55–61; Pardoux and Peng, Lecture Notes in Control and Information Sciences 176 (1992) 200–217]. We have at our disposal stochastic processes which solve the so-called backward stochastic differential equations. These processes provide us with a Feynman-Kac representation for the solutions of a class of nonlinear partial differential equations (PDEs) which appear in many applications in the field of Mathematical Finance. Therefore there is a great interest among both practitioners and theoreticians to develop reliable numerical methods for their numerical resolution. In this survey, we present a number of probabilistic methods for approximating solutions of semilinear PDEs all based on the corresponding Feynman-Kac representation. We also include a general introduction to backward stochastic differential equations and their connection with PDEs and provide a generic framework that accommodates existing probabilistic algorithms and facilitates the construction of new ones.
Mathematics Subject Classification: 65C30 / 65C05 / 60H07 / 62G08
Key words: Probabilistic methods / semilinear PDEs / BSDEs / Monte Carlo methods / Malliavin calculus / cubature methods
© EDP Sciences, SMAI, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.