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Markovian projections for It\^o semimartingales with jumps

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  • Martin Larsson
  • Shukun Long

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.

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  • Martin Larsson & Shukun Long, 2024. "Markovian projections for It\^o semimartingales with jumps," Papers 2403.15980, arXiv.org.
    • Handle: RePEc:arx:papers:2403.15980
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    References listed on IDEAS

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    1. Aurélien Alfonsi & Céline Labart & Jérôme Lelong, 2016. "Stochastic Local Intensity Loss Models With Interacting Particle Systems," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 366-394, April.
    2. Frédéric Abergel & Rémi Tachet, 2010. "A nonlinear partial integro-differential equation from mathematical finance," Post-Print hal-00611962, HAL.
    3. Benjamin Jourdain & Alexandre Zhou, 2020. "Existence of a calibrated regime switching local volatility model," Mathematical Finance, Wiley Blackwell, vol. 30(2), pages 501-546, April.
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