| Abstract: |
| In this talk, we consider optimal control problems of stochastic Volterra equations (SVEs) with singular kernels and general (non-convex) control domain, and demonstrate a general maximum principle by means of the spike variation technique. We first show a Taylor type expansion of the controlled SVE with respect to the spike variation, where the convergence rates of the expansions are characterized by the singularity of the kernel. Next, assuming that the kernel is completely monotone, we convert the variational SVEs appearing in the expansion to their infinite-dimensional lifts. Then, we derive new kinds of first and second order adjoint equations in the infinite-dimensional framework and obtain a necessary condition for optimal controls. Furthermore, we discuss some relationships between the infinite dimensional adjoint equations and backward stochastic Volterra integral equations. |
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