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Backward Stochastic Difference Equations for a Single Jump Process

Author

Listed:
  • Leo Shen

    (University of Adelaide)

  • Robert J. Elliott

    (University of Adelaide
    University of Calgary)

Abstract

We define Backward Stochastic Difference Equations related to a discrete finite time single jump process. We prove the existence and uniqueness of solutions under some assumptions. A comparison theorem for these solutions is also given. Applications to the theory of nonlinear expectations are then investigated. In this paper the single jump process takes values in a general measurable space where as previous work has considered the situation where the noise is a finite state Markov chain, so the state space is finite.

Suggested Citation

  • Leo Shen & Robert J. Elliott, 2012. "Backward Stochastic Difference Equations for a Single Jump Process," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 955-971, December.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:4:d:10.1007_s11009-011-9217-z
    DOI: 10.1007/s11009-011-9217-z
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    References listed on IDEAS

    as
    1. Cohen, Samuel N. & Elliott, Robert J., 2010. "A general theory of finite state Backward Stochastic Difference Equations," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 442-466, April.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
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