TY - GEN

T1 - Second order backward SDEs, fully nonlinear PDEs, and applications in finance

AU - Touzi, Nizar

PY - 2010

Y1 - 2010

N2 - 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 fully-nonlinear Cauchy problem, and is motivated by applications in finance and probabilistic numerical methods for PDEs.

AB - 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 fully-nonlinear Cauchy problem, and is motivated by applications in finance and probabilistic numerical methods for PDEs.

KW - Backward stochastic differential equations

KW - Non-dominated mutually singular measures

KW - Stochastic analysis

KW - Viscosity solutions of second order PDEs

UR - http://www.scopus.com/inward/record.url?scp=84874257283&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874257283&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84874257283

SN - 9814324302

SN - 9789814324304

T3 - Proceedings of the International Congress of Mathematicians 2010, ICM 2010

SP - 3132

EP - 3150

BT - Proceedings of the International Congress of Mathematicians 2010, ICM 2010

T2 - International Congress of Mathematicians 2010, ICM 2010

Y2 - 19 August 2010 through 27 August 2010

ER -