Markovian projections for It\^o semimartingales with jumps
Probability
2024-03-26 v1 Mathematical Finance
Abstract
Given a general It\^o semimartingale, its Markovian projection is an It\^o process, with Markovian differential characteristics, that matches the one-dimensional marginal laws of the original process. We construct Markovian projections for It\^o semimartingales with jumps, whose flows of one-dimensional marginal laws are solutions to non-local Fokker--Planck--Kolmogorov equations (FPKEs). As an application, we show how Markovian projections appear in building calibrated diffusion/jump models with both local and stochastic features.
Cite
@article{arxiv.2403.15980,
title = {Markovian projections for It\^o semimartingales with jumps},
author = {Martin Larsson and Shukun Long},
journal= {arXiv preprint arXiv:2403.15980},
year = {2024}
}