Abstract
In this chapter we discuss so-called “backward stochastic differential equations”, BSDEs for short. Linear BSDEs first appeared a 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 Proposition 5.31 below). However, the first published paper on nonlinear BSDEs, appeared only in 1990, see Pardoux and Peng [51]. Since then, the interest in BSDEs has increased regularly, due to the connections of this subject with mathematical finance, stochastic control, and partial differential equations.
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