Backward Stochastic Partial Differential Equations and their Application to Stochastic Black-Scholes Formula

Qi Zhang (Fudan University)
Thursday, July 17, 2014 - 4:00pm
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041

The backward SPDEs, originated from the study of optimal control theory of SPDEs, can be applied to mathematical finance problems. We demonstrate their theoretical application to stochastic Black-Scholes formula, in a general setting to the parameters of the model. This application is based on our studies of the solvability to degenerate backward SPDEs without technical assumptions and their connection with forward-backward SDEs. The connection between backward SPDEs and forward-backward SDEs can also be regarded as an extension of Feynman-Kac formula to non-Markovian framework.