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Computing the exit-time for a finite-range symmetric jump process

Author

Listed:
  • Burch Nathanial

    (Department of Mathematics, Gonzaga University, 502 E. Boone Ave. MSC 2615, Spokane, WA 99258, USA)

  • Lehoucq R. B.

    (Sandia National Laboratories, P.O. Box 5800, MS 1320, Albuquerque, NM 87185–1320, USA)

Abstract

This paper investigates the exit-time for a broad class of symmetric finite-range jump processes via the corresponding master equation, a nonlocal diffusion equation suitably constrained. In direct analogy to the classical diffusion equation with a homogeneous Dirichlet boundary condition, the nonlocal diffusion equation is augmented with a homogeneous volume-constraint. The volume-constrained master equation provides an efficient alternative over Monte Carlo simulation for computing an important statistic of the process. Several numerical examples are given.

Suggested Citation

  • Burch Nathanial & Lehoucq R. B., 2015. "Computing the exit-time for a finite-range symmetric jump process," Monte Carlo Methods and Applications, De Gruyter, vol. 21(2), pages 139-152, June.
    • Handle: RePEc:bpj:mcmeap:v:21:y:2015:i:2:p:139-152:n:3
    DOI: 10.1515/mcma-2014-0015
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    References listed on IDEAS

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    1. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1, July-Dece.
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