FEEDBACK OPTIMAL CONTROL FOR STOCHASTIC VOLTERRA EQUATIONS WITH COMPLETELY MONOTONE KERNELS

作者：Confortola Fulvia^*; Mastrogiacomo Elisa

来源：Mathematical Control and Related Fields, 2015, 5(2): 191-235.

DOI：10.3934/mcrf.2015.5.191

• Stochastic Volterra integral equation
• backward stochastic differential equations
• optimal control
• HJB equation
• feedback law

In this paper we are concerned with a class of stochastic Volterra integro-differential problems with completely monotone kernels, where we assume that the noise enters the system when we introduce a control. We start by reformulating the state equation into a semilinear evolution equation which can be treated by semigroup methods. The application to optimal control provides other interesting results and requires a precise description of the properties of the generated semigroup.
The first main result of the paper is the proof of existence and uniqueness of a mild solution for the corresponding Hamilton-Jacobi-Bellman (HJB) equation. The main technical point consists in the differentiability of the BSDE associated with the reformulated equation with respect to its initial datum x.

• 出版日期2015-6