Holomorphic jump-diffusions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917829814517760 |
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| author | Cuchiero, Christa Primavera, Francesca Svaluto-Ferro, Sara |
| author_facet | Cuchiero, Christa Primavera, Francesca Svaluto-Ferro, Sara |
| contents | We introduce a class of jump-diffusions, called holomorphic, of which the well-known classes of affine and polynomial processes are particular instances. The defining property concerns the extended generator, which is required to map a (subset of) holomorphic functions to themselves. This leads to a representation of the expectation of power series of the process' marginals via a potentially infinite dimensional linear ODE. We apply the same procedure by considering exponentials of holomorphic functions, leading to a class of processes named affine-holomorphic for which a representation for quantities as the characteristic function of power series is provided. Relying on powerful results from complex analysis, we obtain sufficient conditions on the process' characteristics which guarantee the holomorphic and affine-holomorphic properties and provide applications to several classes of jump-diffusions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04238 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holomorphic jump-diffusions Cuchiero, Christa Primavera, Francesca Svaluto-Ferro, Sara Probability 60G20, 60J76, 37F80 We introduce a class of jump-diffusions, called holomorphic, of which the well-known classes of affine and polynomial processes are particular instances. The defining property concerns the extended generator, which is required to map a (subset of) holomorphic functions to themselves. This leads to a representation of the expectation of power series of the process' marginals via a potentially infinite dimensional linear ODE. We apply the same procedure by considering exponentials of holomorphic functions, leading to a class of processes named affine-holomorphic for which a representation for quantities as the characteristic function of power series is provided. Relying on powerful results from complex analysis, we obtain sufficient conditions on the process' characteristics which guarantee the holomorphic and affine-holomorphic properties and provide applications to several classes of jump-diffusions. |
| title | Holomorphic jump-diffusions |
| topic | Probability 60G20, 60J76, 37F80 |
| url | https://arxiv.org/abs/2411.04238 |