Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order

Abstract

The aim of this article is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semilinear second order partial differential equations of parabolic and elliptic type, in short PDEs. Linear BSDEs appeared long time ago, both as the equations for the adjoint process in stochastic control, as well as the model behind the Black and Scholes formula for the pricing and hedging of options in mathematical finance. These linear BSDEs can be solved more or less explicitly (see proof of Theorem 1.4).