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Forward - backward stochastic differential equations with random coeffcients and applications to finance
(13-07-2016) Kartala, Xanthi-Isidora; Athens University of Economics and Business, Department of Statistics; Yannacopoulos, Athanasios
The first part of this thesis studies forward and backward versions of the random Burgers equation (RBE) with stochastic coeffcients. First, the celebrated Cole-Hopf transformation reduces the forward RBE to a forward random heat equation (RHE) that can be treated pathwise. Next we provide a connection between the backward Burgers equation and a system of forward backward stochastic differential equations (FBSDEs). Exploiting this connection, we derive a generalization of the Cole-Hopf transformation which links the backward RBE with the backward RHE and investigate the range of its applicability. Stochastic Feynman- Kac representations for the solutions are provided. Explicit solutions are constructed and applications to stochastic control and mathematical finance are discussed.