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Inverting the Markovian projection for pure jump processes

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  • Larsson, Martin
  • Long, Shukun

Abstract

Markovian projections arise in problems where we aim to mimic the one-dimensional marginal laws of an Itô semimartingale by using another Itô process with Markovian dynamics. In applications, Markovian projections are useful in calibrating jump–diffusion models with both local and stochastic features, leading to the study of the inversion problems. In this paper, we invert the Markovian projections for pure jump processes, which can be used to construct calibrated local stochastic intensity (LSI) models for credit risk applications. Such models are jump process analogues of the notoriously hard to construct local stochastic volatility (LSV) models used in equity modeling.

Suggested Citation

  • Larsson, Martin & Long, Shukun, 2026. "Inverting the Markovian projection for pure jump processes," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002480
    DOI: 10.1016/j.spa.2025.104804
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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.
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