Marco Fuhrman: A control randomization method in stochastic optimal control and BSDEs with constrained jumps

Abstract

 We present an approach to stochastic optimal control problems, originally introduced by B. Bouchard and then developed by many others, which allows to represent the value of large classes of optimization problems by means of a Backward Stochastic Differential Equation (BSDE).

It consists in replacing the original problem with an auxiliary, equivalent one, where the control process is replaced by a fixed random process and a new optimization is performed over changes of probability measures. A BSDE is then introduced in order to represent the value of both optimization problems. In the Markovian framework this method also covers cases when the associated Hamilton-Jacobi-Bellman equation is fully non-linear.