Explicit Asymptotics on First Passage Times of Diffusion Processes
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866912820425129984 |
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| author | Dassios, Angelos Li, Luting |
| author_facet | Dassios, Angelos Li, Luting |
| contents | We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for probability densities of single-sided level crossing problem. The framework is applicable to diffusion processes with continuous drift functions, and a recursive system in the frequency domain has been provided. Besides, we derive a probabilistic representation for error estimation. The representation can be used to evaluate deviations in perturbed density functions. In the present paper, we apply the framework to Ornstein-Uhlenbeck and Bessel processes to find closed-form approximations for their first passage times; another successful application is given by the exponential-Shiryaev process. Numerical results are provided at the end of this paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1806_08161 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Explicit Asymptotics on First Passage Times of Diffusion Processes Dassios, Angelos Li, Luting Probability Numerical Analysis Mathematical Finance 91G60, 60G40, 62E17, 91G80 We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for probability densities of single-sided level crossing problem. The framework is applicable to diffusion processes with continuous drift functions, and a recursive system in the frequency domain has been provided. Besides, we derive a probabilistic representation for error estimation. The representation can be used to evaluate deviations in perturbed density functions. In the present paper, we apply the framework to Ornstein-Uhlenbeck and Bessel processes to find closed-form approximations for their first passage times; another successful application is given by the exponential-Shiryaev process. Numerical results are provided at the end of this paper. |
| title | Explicit Asymptotics on First Passage Times of Diffusion Processes |
| topic | Probability Numerical Analysis Mathematical Finance 91G60, 60G40, 62E17, 91G80 |
| url | https://arxiv.org/abs/1806.08161 |