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arXiv · 2403.15980

Markovian projections for Itô semimartingales with jumps

Martin Larsson·Shukun Long
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Abstract

Given a general Itô semimartingale, its Markovian projection is an Itô process, with Markovian differential characteristics, that matches the one-dimensional marginal laws of the original process. We construct Markovian projections for Itô 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.

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Martin Larsson, Shukun Long. 2024-03-24. Markovian projections for Itô semimartingales with jumps. https://arxiv.org/abs/2403.15980

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