Markovian projections for functionals of It\^o semimartingales with jumps
Probability
2026-05-26 v2 Mathematical Finance
Abstract
Given an It\^o semimartingale , its Markovian projection is an It\^o semimartingale , with Markovian differential characteristics, that matches the one-dimensional marginal laws of . 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 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 It\^o semimartingales with jumps.
Keywords
Cite
@article{arxiv.2506.00762,
title = {Markovian projections for functionals of It\^o semimartingales with jumps},
author = {Martin Larsson and Shukun Long},
journal= {arXiv preprint arXiv:2506.00762},
year = {2026}
}