Optimal targeting position and (forward) backward stochastic differential equation
In this talk we present an optimal stochastic control problem related to portfolio liquidation problems. For the homogeneous case, we give a complete solution using backward stochastic differential equation with singular terminal condition (joint work with T. Kruse (Essen, Germany)). In the Brownian setting, we explain how it can be (partially) solved using forward backward SDE together with the decoupling field method (work in progress with S. Ankirchner, A. Fromm (Jena, Germany) and T. Kruse (Essen, Germany)). At the end we will generalize this problem under Knightian uncertainty (joint paper with C. Zhou (NUS, Singapore)).