Optimal stopping of an Ornstein-Uhlenbeck bridge
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909221178572800 |
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| author | Azze, Abel D'Auria, Bernardo García-Portugués, Eduardo |
| author_facet | Azze, Abel D'Auria, Bernardo García-Portugués, Eduardo |
| contents | We make a rigorous analysis of the existence and characterization of the free boundary related to the optimal stopping problem that maximizes the mean of an Ornstein--Uhlenbeck bridge. The result includes the Brownian bridge problem as a limit case. The methodology hereby presented relies on a time-space transformation that casts the original problem into a more tractable one with an infinite horizon and a Brownian motion underneath. We comment on two different numerical algorithms to compute the free-boundary equation and discuss illustrative cases that shed light on the boundary's shape. In particular, the free boundary generally does not share the monotonicity of the Brownian bridge case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_13056 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Optimal stopping of an Ornstein-Uhlenbeck bridge Azze, Abel D'Auria, Bernardo García-Portugués, Eduardo Probability 60G40, 60J60 We make a rigorous analysis of the existence and characterization of the free boundary related to the optimal stopping problem that maximizes the mean of an Ornstein--Uhlenbeck bridge. The result includes the Brownian bridge problem as a limit case. The methodology hereby presented relies on a time-space transformation that casts the original problem into a more tractable one with an infinite horizon and a Brownian motion underneath. We comment on two different numerical algorithms to compute the free-boundary equation and discuss illustrative cases that shed light on the boundary's shape. In particular, the free boundary generally does not share the monotonicity of the Brownian bridge case. |
| title | Optimal stopping of an Ornstein-Uhlenbeck bridge |
| topic | Probability 60G40, 60J60 |
| url | https://arxiv.org/abs/2110.13056 |