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Stochastic Local Intensity Loss Models with Interacting Particle Systems

Author

Listed:
  • Aurélien Alfonsi

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTech)

  • Céline Labart

    (LAMA - Laboratoire de Mathématiques - USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc - CNRS - Centre National de la Recherche Scientifique)

  • Jérôme Lelong

    (DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA [2016-2019] - Université Grenoble Alpes [2016-2019])

Abstract

It is well-known from the work of Schönbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The Stochastic Local Intensity (SLI) models such as the one proposed by Arnsdorf and Halperin (2008) allow to get a stochastic jump intensity while keeping the same marginal laws. These models involve a non-linear SDE with jumps. The first contribution of this paper is to prove the existence and uniqueness of such processes. This is made by means of an interacting particle system, whose convergence rate towards the non-linear SDE is analyzed. Second, this approach provides a powerful way to compute pathwise expectations with the SLI model: we show that the computational cost is roughly the same as a crude Monte-Carlo algorithm for standard SDEs.

Suggested Citation

  • Aurélien Alfonsi & Céline Labart & Jérôme Lelong, 2016. "Stochastic Local Intensity Loss Models with Interacting Particle Systems," Post-Print hal-00786239, HAL.
    • Handle: RePEc:hal:journl:hal-00786239
    DOI: 10.1111/mafi.12059
    Note: View the original document on HAL open archive server: https://hal.science/hal-00786239
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