Efficient simulation of a new class of Volterra-type SDEs
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914081872543744 |
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| author | Bonesini, Ofelia Callegaro, Giorgia Grasselli, Martino Pagès, Gilles |
| author_facet | Bonesini, Ofelia Callegaro, Giorgia Grasselli, Martino Pagès, Gilles |
| contents | We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go back, i.e., the transformation is reversible. We discuss existence and path-wise regularity of solutions for our class of stochastic differential equations. In the fractional kernel case, when $H \in (0,\frac12)$, where $H$ is the Hurst coefficient, we propose a numerical simulation scheme which exhibits a remarkable strong convergence rate of order $1/2$, which constitutes a bold improvement when compared with the performance of available Euler schemes, whose strong rate of convergence is $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02708 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient simulation of a new class of Volterra-type SDEs Bonesini, Ofelia Callegaro, Giorgia Grasselli, Martino Pagès, Gilles Mathematical Finance Probability 60G22, 65C20, 91G60 We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go back, i.e., the transformation is reversible. We discuss existence and path-wise regularity of solutions for our class of stochastic differential equations. In the fractional kernel case, when $H \in (0,\frac12)$, where $H$ is the Hurst coefficient, we propose a numerical simulation scheme which exhibits a remarkable strong convergence rate of order $1/2$, which constitutes a bold improvement when compared with the performance of available Euler schemes, whose strong rate of convergence is $H$. |
| title | Efficient simulation of a new class of Volterra-type SDEs |
| topic | Mathematical Finance Probability 60G22, 65C20, 91G60 |
| url | https://arxiv.org/abs/2306.02708 |