Second Order Backward SDEs, Fully Nonlinear PDEs, and Applications in Finance

Nizar Touzi
2011 Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)  
The martingale representation theorem in a Brownian filtration represents any square integrable r.v. ξ as a stochastic integral with respect to the Brownian motion. This is the simplest Backward SDE with nul generator and final data ξ, which can be seen as the non-Markov counterpart of the Cauchy problem in second order parabolic PDEs. Similarly, the notion of Second order BSDEs is the non-Markov counterpart of the fullynonlinear Cauchy problem, and is motivated by applications in finance and
more » ... ns in finance and probabilistic numerical methods for PDEs. (2000) . Primary 60H10; Secondary 60H30. Mathematics Subject Classification Keywords. Backward stochastic differential equations, stochastic analysis, non-dominated mutually singular measures, viscosity solutions of second order PDEs. * Based on a long collaboration with Mete
doi:10.1142/9789814324359_0183 fatcat:ruw3cmpvyzhbxlw6wqzqxlfe7u