Lifting of Volterra processes: optimal control in UMD Banach spaces
Optimization and Control
2023-06-27 v1
Abstract
We study a stochastic control problem for a Volterra-type controlled forward equation with past dependence obtained via convolution with a deterministic kernel. To be able to apply dynamic programming to solve the problem, we lift it to infinite dimensions and we formulate a UMD Banach-valued Markovian problem, which is shown to be equivalent to the original finite-dimensional non-Markovian one. We characterize the optimal control for the infinite dimensional problem and show that this also characterizes the optimal control for the finite dimensional problem.
Keywords
Cite
@article{arxiv.2306.14175,
title = {Lifting of Volterra processes: optimal control in UMD Banach spaces},
author = {Giulia di Nunno and Michele Giordano},
journal= {arXiv preprint arXiv:2306.14175},
year = {2023}
}