The objective of this talk is to present a stochastic maximum principle for a control problem with a criterion implicitly defined by a quadratic BSDE. Quadratic growth BSDEs are well studied objects and their systematic study started with the seminal work of M. Kobilansky in 2000. Convex and quadratic BSDEs are related to risk aversion and utility models. As such, they naturally appear to represent criteria of utility maximization problems.However, since the seminal work of J-M. Bismut on stochastic maximum principle for control problems (and following works by A. Bensoussan, S. Peng etc…), a specific study of the quadratic case seems missing in the literature. The first part of the talk is dedicated to an introduction to BSDEs and quadratic BSDEs. We present essential tools to study BSDEs and we explain the link with risk measures and utility models. In the second part of the presentation a stochastic maximum principle is established for a risk averse control problem modeled via a quadratic BSDE. Finally we discuss potential applications to mean field games and mean field control problems.

https://indico.math.cnrs.fr/event/10975/