Stochastic dynamics in financial modeling

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In modeling financial variables mathematically it is important to consider dynamics which lead to tractable solutions while at the same time capture qualitative features of empirical data. The proposed research program involves the study of various stochastic equations, their properties, and their application to modeling in finance. In particular we shall focus on the pricing and hedging of various term-structure derivatives, commodity contracts, default (credit) risk, and insurance products. Attention shall also be given to the foundations and analytic tools necessary to implement the models effectively. The main class of stochastic equations to be considered are forward-backward stochastic differential equations (FBSDEs, for short). A FBSDE is a coupled system of stochastic equations of which certain components evolve forward in time from an initial condition and other components evolve backward in time from a random terminal condition. Several problems in the literature have been solved by characterizing financial models in terms of FBSDEs.