Exponential utility maximization and BSDEs with quadratic growth.

This talk is devoted to the study of the problem of
the exponential utility maximization by
the BSDE approach. Firstly, in an informal manner,
we deduce a quadratic BSDE linked with
the exponential utility maximization problem.
Then we study this introduced BSDE. Finally,
we apply the result on BSDE to derive both
the existence of optimal trading strategy and the
optimal value of utility. As opposed to most
of the papers dealing with this subject, the investors’
trading strategies we allow underly constraints
described by closed, but not necessarily convex, sets.