Stochastic control with self-exciting processes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911674217267200 |
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| author | Eyjolfsson, Heidar Dahl, Kristina Rognlien |
| author_facet | Eyjolfsson, Heidar Dahl, Kristina Rognlien |
| contents | We analyze the problem of stochastic optimal control of SDEs where the driver includes a self-exciting stochastic process. Due to the non-Markovian nature of the problem, we apply the stochastic maximum principle approach. We derive a sufficient stochastic maximum principle under this framework. We also derive an expression via martingales of both the self-exciting process and its quadratic covariation. Furthermore, we derive a necessary maximum (equivalence principle) for the self-exciting stochastic control problem. Finally, we look at an application to log-utility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12035 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic control with self-exciting processes Eyjolfsson, Heidar Dahl, Kristina Rognlien Optimization and Control Probability 93E20, 49J55, 60G55 We analyze the problem of stochastic optimal control of SDEs where the driver includes a self-exciting stochastic process. Due to the non-Markovian nature of the problem, we apply the stochastic maximum principle approach. We derive a sufficient stochastic maximum principle under this framework. We also derive an expression via martingales of both the self-exciting process and its quadratic covariation. Furthermore, we derive a necessary maximum (equivalence principle) for the self-exciting stochastic control problem. Finally, we look at an application to log-utility. |
| title | Stochastic control with self-exciting processes |
| topic | Optimization and Control Probability 93E20, 49J55, 60G55 |
| url | https://arxiv.org/abs/2605.12035 |