Title: Multidimensional linear-quadratic control with terminal constraints and singular BSDEs
Abstract: Control problems with terminal constraints and noise arise in applications in engineering and finance. A tool to analyse such problems, but also of interest on their own and in connection to partial differential equations, are backward stochastic differential equations (BSDEs). In particular, some one-dimensional stochastic optimal control problems with terminal constraints have been characterised in terms of BSDEs with singular terminal conditions.
In this talk, we address a class of terminally constrained multidimensional linear-quadratic stochastic optimal control problems. The problem features matrix-valued stochastic coefficients, the state dynamics are non-diffusive and the terminal state is restricted to a prescribed random linear subspace. Using a penalisation approach, we obtain a solution to this constrained multidimensional problem, now involving a matrix-valued BSDE with an appropriately defined singular terminal condition. We establish the existence of a minimal supersolution to this BSDE and explain how it can be used to describe both the value function and the optimal control.
The talk is based on joint work with Thomas Kruse, Petr Petrov and Alexandre Popier.