Linear–quadratic stochastic Volterra controls I: Causal feedback strategies

Yushi Hamaguchi and Tianxiao Wang

Stochastic Processes and their Applications, 2024, vol. 176, issue C

Abstract: In this paper, we formulate and investigate the notion of causal feedback strategies arising in linear–quadratic control problems for stochastic Volterra integral equations (SVIEs) with singular and non-convolution-type coefficients. We show that there exists a unique solution, which we call the causal feedback solution, to the closed-loop system of a controlled SVIE associated with a causal feedback strategy. Furthermore, introducing two novel equations named a Type-II extended backward stochastic Volterra integral equation and a Lyapunov–Volterra equation, we prove a duality principle and a representation formula for a quadratic functional of controlled SVIEs in the framework of causal feedback strategies.

Keywords: Linear–Quadratic control; Stochastic Volterra integral equation; Causal feedback strategy (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104449

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