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 -