Feller's test for explosions of stochastic Volterra equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910495280201728 |
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| author | Bondi, Alessandro Pulido, Sergio |
| author_facet | Bondi, Alessandro Pulido, Sergio |
| contents | This paper provides a Feller's test for explosions of one-dimensional continuous stochastic Volterra processes of convolution type. The study focuses on dynamics governed by nonsingular kernels, which preserve the semimartingale property of the processes and introduce memory features through a path-dependent drift. In contrast to the classical path-independent case, the sufficient condition derived in this study for a Volterra process to remain in the interior of an interval is generally more restrictive than the necessary condition. The results are illustrated with three specifications of the dynamics: the Volterra square-root diffusion, the Volterra Jacobi process and the Volterra power-type diffusion. For the Volterra square-root diffusion, also known as the Volterra CIR process, the paper presents a detailed discussion on the approximation of the singular fractional kernel with a sum of exponentials, a method commonly employed in the mathematical finance literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_13537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Feller's test for explosions of stochastic Volterra equations Bondi, Alessandro Pulido, Sergio Probability 60H20, 45D05, 60K50 This paper provides a Feller's test for explosions of one-dimensional continuous stochastic Volterra processes of convolution type. The study focuses on dynamics governed by nonsingular kernels, which preserve the semimartingale property of the processes and introduce memory features through a path-dependent drift. In contrast to the classical path-independent case, the sufficient condition derived in this study for a Volterra process to remain in the interior of an interval is generally more restrictive than the necessary condition. The results are illustrated with three specifications of the dynamics: the Volterra square-root diffusion, the Volterra Jacobi process and the Volterra power-type diffusion. For the Volterra square-root diffusion, also known as the Volterra CIR process, the paper presents a detailed discussion on the approximation of the singular fractional kernel with a sum of exponentials, a method commonly employed in the mathematical finance literature. |
| title | Feller's test for explosions of stochastic Volterra equations |
| topic | Probability 60H20, 45D05, 60K50 |
| url | https://arxiv.org/abs/2406.13537 |