A Probabilistic Approach for Discontinuous Coeffcients FBSDEs and PDEs

This thesis is about discussing solvability of coupled forward backward stochastic differential equations (FBSDEs) and quasilinear parabolic partial differential equations (PDEs) with all the coefficients allowed to be discontinuous. Our work provides numerous conditions for existence and uniqueness results via a probabilistic method related to Girsanov transform. Also, we provide two related practical applications: optimal control of the spread of infectious disease and carbon allowance pricing.