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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.18394 |
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| _version_ | 1866910966690611200 |
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| author | Rodosthenous, Neofytos Zervos, Mihail |
| author_facet | Rodosthenous, Neofytos Zervos, Mihail |
| contents | The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running maximum processes. In its original form, the maximality principle identifies an optimal stopping boundary function as the maximal solution to a specific first-order nonlinear ODE that stays strictly below the diagonal in $\mathbb{R}^2$. In the context of a suitably tailored optimal stopping problem, we derive a substantial generalisation of the maximality principle: the optimal stopping boundary function is the maximal solution to a specific first-order nonlinear ODE that is associated with a solution to the optimal stopping problem's variational inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18394 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal stopping involving a diffusion and its running maximum: a generalisation of the maximality principle Rodosthenous, Neofytos Zervos, Mihail Probability 60G40, 60H30, 49J10, 49K10, 93E20 The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running maximum processes. In its original form, the maximality principle identifies an optimal stopping boundary function as the maximal solution to a specific first-order nonlinear ODE that stays strictly below the diagonal in $\mathbb{R}^2$. In the context of a suitably tailored optimal stopping problem, we derive a substantial generalisation of the maximality principle: the optimal stopping boundary function is the maximal solution to a specific first-order nonlinear ODE that is associated with a solution to the optimal stopping problem's variational inequality. |
| title | Optimal stopping involving a diffusion and its running maximum: a generalisation of the maximality principle |
| topic | Probability 60G40, 60H30, 49J10, 49K10, 93E20 |
| url | https://arxiv.org/abs/2505.18394 |