Markov approximation for controlled Hawkes Jump-Diffusions with general kernels
Probability
2025-07-16 v1 Optimization and Control
Abstract
We present a Markov approximation for jump-diffusions whose jump part consists in a Hawkes process with intensity driven by a general (possibly non-monotone) kernel. Under minimal integrability conditions, the kernel can be approximated by a linear combination of exponential functions. This implies that Hawkes jump-diffusions can be approximated with Markov jump-diffusions. We illustrate the usefulness of this approximation by applying it to a class of stochastic control problems.
Cite
@article{arxiv.2507.11294,
title = {Markov approximation for controlled Hawkes Jump-Diffusions with general kernels},
author = {Mahmoud Khabou and Mehdi Talbi},
journal= {arXiv preprint arXiv:2507.11294},
year = {2025}
}