Markovian projections for functionals of Itô semimartingales with jumps
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| Format: | Preprint |
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2025
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| _version_ | 1866916041775382528 |
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| author | Larsson, Martin Long, Shukun |
| author_facet | Larsson, Martin Long, Shukun |
| contents | Given an Itô semimartingale $X$, its Markovian projection is an Itô semimartingale $\widehat{X}$, with Markovian differential characteristics, that matches the one-dimensional marginal laws of $X$. One may even require certain functionals of the two processes to have the same fixed-time marginals, at the cost of enhancing the differential characteristics of $\widehat{X}$ but still in a Markovian sense. In the continuous case, the definitive result on existence of Markovian projections was obtained by Brunick and Shreve~\cite{MR3098443}. In this paper, we extend their result to the fully general setting of Itô semimartingales with jumps. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_00762 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Markovian projections for functionals of Itô semimartingales with jumps Larsson, Martin Long, Shukun Probability Mathematical Finance Given an Itô semimartingale $X$, its Markovian projection is an Itô semimartingale $\widehat{X}$, with Markovian differential characteristics, that matches the one-dimensional marginal laws of $X$. One may even require certain functionals of the two processes to have the same fixed-time marginals, at the cost of enhancing the differential characteristics of $\widehat{X}$ but still in a Markovian sense. In the continuous case, the definitive result on existence of Markovian projections was obtained by Brunick and Shreve~\cite{MR3098443}. In this paper, we extend their result to the fully general setting of Itô semimartingales with jumps. |
| title | Markovian projections for functionals of Itô semimartingales with jumps |
| topic | Probability Mathematical Finance |
| url | https://arxiv.org/abs/2506.00762 |