Lifting of Volterra processes: optimal control in UMD Banach spaces

Giulia Di Nunno; Michele Giordano

Lifting of Volterra processes: optimal control in UMD Banach spaces

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arxiv 2306.14175 v1 pith:TXI5SSCU submitted 2023-06-25 math.OC

Giulia di Nunno , Michele Giordano This is my paper · ORCID

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keywords problemcontroloptimaldimensionalinfiniteableapplybanach

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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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Markov approximation for controlled Hawkes Jump-Diffusions with general kernels
math.PR 2025-07 conditional novelty 5.0 of 10

Any Hawkes jump-diffusion with an integrable kernel can be approximated arbitrarily well by an augmented Markov jump-diffusion, and optimal control values converge under the same approximation.

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