Markovian projections for functionals of Itô semimartingales with jumps

Fuente: arXiv
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Main Authors: Larsson, Martin, Long, Shukun
Format: Preprint
Published: 2025
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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
id 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