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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.05025 |
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| _version_ | 1866911422249697280 |
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| author | Agostino, Isabel Mastrolia, Thibaut |
| author_facet | Agostino, Isabel Mastrolia, Thibaut |
| contents | We investigate a singular-optimal stopping stochastic control problem driven by self-exciting dynamics governed by a Hawkes process. In the continuous-time setting, we show that the optimization problem reduces to solving a variational partial differential equation with gradient constraints. We then introduce its discrete-time counterpart, modeled as a Markov Decision Process. We prove that, under an appropriate rescaling procedure, the value function of the discrete-time problem converges to its continuous-time equivalent, implying that the discrete-time optimizers are asymptotically optimal for the continuous-time problem. Finally, we apply these results to an Ornstein-Uhlenbeck stochastic differential equation driven by a Hawkes process with singular control, motivated by optimal power plant investment under cyber threat and we illustrate the theoretical findings through numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05025 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Approximation of Singular-Stopping Control Driven by Hawkes Processes via Rescaled MDPs Agostino, Isabel Mastrolia, Thibaut Optimization and Control Probability We investigate a singular-optimal stopping stochastic control problem driven by self-exciting dynamics governed by a Hawkes process. In the continuous-time setting, we show that the optimization problem reduces to solving a variational partial differential equation with gradient constraints. We then introduce its discrete-time counterpart, modeled as a Markov Decision Process. We prove that, under an appropriate rescaling procedure, the value function of the discrete-time problem converges to its continuous-time equivalent, implying that the discrete-time optimizers are asymptotically optimal for the continuous-time problem. Finally, we apply these results to an Ornstein-Uhlenbeck stochastic differential equation driven by a Hawkes process with singular control, motivated by optimal power plant investment under cyber threat and we illustrate the theoretical findings through numerical simulations. |
| title | Approximation of Singular-Stopping Control Driven by Hawkes Processes via Rescaled MDPs |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2602.05025 |