A high-order recombination algorithm for weak approximation of stochastic differential equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910952780201984 |
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| author | Ninomiya, Syoiti Shinozaki, Yuji |
| author_facet | Ninomiya, Syoiti Shinozaki, Yuji |
| contents | This paper presents an algorithm for applying the high-order recombination method, originally introduced by Lyons and Litterer in ``High-order recombination and an application to cubature on Wiener space'' (Ann. Appl. Probab. 22(4):1301--1327, 2012), to practical problems in mathematical finance. A refined error analysis is provided, yielding a sharper condition for space partitioning. Based on this condition, a computationally feasible recursive partitioning algorithm is developed. Numerical examples are also included, demonstrating that the proposed algorithm effectively avoids the explosive growth in the cardinality of the support required to achieve high-order approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A high-order recombination algorithm for weak approximation of stochastic differential equations Ninomiya, Syoiti Shinozaki, Yuji Probability Computational Finance 91G60, 60H35, 65C20, 65C30, 65C05, 68U20, 62P05 This paper presents an algorithm for applying the high-order recombination method, originally introduced by Lyons and Litterer in ``High-order recombination and an application to cubature on Wiener space'' (Ann. Appl. Probab. 22(4):1301--1327, 2012), to practical problems in mathematical finance. A refined error analysis is provided, yielding a sharper condition for space partitioning. Based on this condition, a computationally feasible recursive partitioning algorithm is developed. Numerical examples are also included, demonstrating that the proposed algorithm effectively avoids the explosive growth in the cardinality of the support required to achieve high-order approximations. |
| title | A high-order recombination algorithm for weak approximation of stochastic differential equations |
| topic | Probability Computational Finance 91G60, 60H35, 65C20, 65C30, 65C05, 68U20, 62P05 |
| url | https://arxiv.org/abs/2504.19717 |