Global maximum principle for optimal control of stochastic Volterra equations with singular kernels

Speaker: Yushi Hamaguchi 
Affiliation: Kyoto University

Abstract

In this talk, we consider optimal control problems of stochastic Volterra equations (SVEs) with singular kernels, where the control domain is not necessarily convex. We establish a global maximum principle by means of the spike variation technique. To do so, we first show a Taylor type expansion of the controlled SVE with respect to the spike variation, where the convergence rates of the remainder terms are characterized by the singularity of the kernels. Next, assuming additional structure conditions for the kernels, we convert the variational SVEs appearing in the expansion to their infinite dimensional lifts. Then, we derive first and second order adjoint equations of the form of infinite dimensional backward stochastic evolution equations (BSEEs), and provide a necessary condition for a given control process to be optimal.