Optimal stopping for Markov processes with positive jumps
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916479497142272 |
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| author | Crocce, Fabian Mordecki, Ernesto |
| author_facet | Crocce, Fabian Mordecki, Ernesto |
| contents | Consider the discounted optimal stopping problem for a real valued Markov process with only positive jumps. We provide a theorem to verify that the optimal stopping region has the form {x >= x^*} for some critical threshold x^*, and a representation formula for the value function of the problem in terms of the Green kernel of the process, based on Dynkin's characterization of the value function as the least excessive majorant. As an application of our results, using the Fourier transform to compute the Green kernel of the process, we solve a new example: the optimal stopping for a Levy-driven Ornstein-Uhlenbeck process used to model prices in electricity markets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08796 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal stopping for Markov processes with positive jumps Crocce, Fabian Mordecki, Ernesto Probability 60G40, 60J25 Consider the discounted optimal stopping problem for a real valued Markov process with only positive jumps. We provide a theorem to verify that the optimal stopping region has the form {x >= x^*} for some critical threshold x^*, and a representation formula for the value function of the problem in terms of the Green kernel of the process, based on Dynkin's characterization of the value function as the least excessive majorant. As an application of our results, using the Fourier transform to compute the Green kernel of the process, we solve a new example: the optimal stopping for a Levy-driven Ornstein-Uhlenbeck process used to model prices in electricity markets. |
| title | Optimal stopping for Markov processes with positive jumps |
| topic | Probability 60G40, 60J25 |
| url | https://arxiv.org/abs/2411.08796 |