Markov approximation for controlled Hawkes Jump-Diffusions with general kernels

2025/07/15 by Mahmoud Khabou, Khabou, Mahmoud, Mehdi Talbi +1 · 1 citation
Mathematics · #45D05 #60G55 #60H10 #93E20 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Optimization and Control (math.OC) #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2507.11294

openalex publication_date 2025/07/15 · openalex created_date 2025/10/08 · openalex updated_date 2026/07/28

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.

Citations

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• Optimal control of Volterra integral diffusions and application to contract theory

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