大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,The University of Osaka

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

Yushi Hamaguchi (Kyoto University)

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

UQ-Osaka Seminar on Financial Mathematics and Economics 第7回 (University of QueenslandとMMDS金融保険部門共催)

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

Yushi Hamaguchi (Kyoto University)

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.