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arXiv · 2306.14175

Lifting of Volterra processes: optimal control in UMD Banach spaces

Giulia di Nunno·Michele Giordano
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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.

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Giulia di Nunno, Michele Giordano. 2023-06-25. Lifting of Volterra processes: optimal control in UMD Banach spaces. https://arxiv.org/abs/2306.14175

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