Singular stochastic optimal control with general coefficients
Ongoing joint work with Yuri Saporito (FGV EMAp) and Agostino Capponi (Columbia University)
In this work, we address singular stochastic control problems in which the coefficients of the singular control in both the dynamics and the cost functional are functions of time, state and the singular control itself. We derive the HJB equation satisfied by the value function, which, as is usual in singular control problems, takes the form of a quasi-variational inequality (QVI). We prove a verification theorem, and are now working on establishing existence and uniqueness of a viscosity solution and approximating it numerically.
