Linear-quadratic stochastic Volterra controls II: Optimal strategies and Riccati--Volterra equations

Abstract

In this paper, we study linear-quadratic control problems for stochastic Volterra integral equations with singular and non-convolution-type coefficients. The weighting matrices in the cost functional are not assumed to be non-negative definite. From a new viewpoint, we formulate a framework of causal feedback strategies. The existence and the uniqueness of a causal feedback optimal strategy are characterized by means of the corresponding Riccati--Volterra equation.

35 pages

References in corpus (2)

• On the maximum principle for optimal control problems of stochastic Volterra integral equations with delay
• Variation of constants formulae for forward and backward stochastic Volterra integral equations