Lecture notes on BSDEs Main existence and stability results

Backward stochastic differential equations (BSDEs) are the non-Markovian (stochastic) counterpart of semi-linear parabolic equations. They have a wide range of applications in economics, and more generally in optimal control. In mathematical finance, the standard hedging theory can be written in terms of BSDEs (possibly reflected or with constraints), but they are also naturally associated to risk measures (g-expectations), utility maximization under constraints, or recursive utilities. These lectures are an introduction to the theory of BSDEs and to their applications. We will concentrate on various existence and stability results, starting from the classical Lipschitz continuous case up to quadratic BSDEs, and BSDEs with constraints. Our aim is to present the techniques rather than the results by themselves, so that the reader can enter the subject and further study the references we provide.

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