Markov approximation for controlled Hawkes Jump-Diffusions with general kernels
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909690035699712 |
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| author | Khabou, Mahmoud Talbi, Mehdi |
| author_facet | Khabou, Mahmoud Talbi, Mehdi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Markov approximation for controlled Hawkes Jump-Diffusions with general kernels Khabou, Mahmoud Talbi, Mehdi Probability Optimization and Control 60G55, 93E20, 45D05, 60H10 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. |
| title | Markov approximation for controlled Hawkes Jump-Diffusions with general kernels |
| topic | Probability Optimization and Control 60G55, 93E20, 45D05, 60H10 |
| url | https://arxiv.org/abs/2507.11294 |