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Discrete Compound Poisson Process with Curved Boundaries: Polynomial Structures and Recursions

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  • Claude Lefèvre

    (Université Libre de Bruxelles)

Abstract

This paper provides a review of recent results, most of them published jointly with Ph. Picard, on the exact distribution of the first crossing of a Poisson or discrete compound Poisson process through a given nondecreasing boundary, of curved or linear shape. The key point consists in using an underlying polynomial structure to describe the distribution, the polynomials being of generalized Appell type for an upper boundary and of generalized Abel–Gontcharoff type for a lower boundary. That property allows us to obtain simple and efficient recursions for the numerical determination of the distribution.

Suggested Citation

  • Claude Lefèvre, 2007. "Discrete Compound Poisson Process with Curved Boundaries: Polynomial Structures and Recursions," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 243-262, June.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:2:d:10.1007_s11009-006-9014-2
    DOI: 10.1007/s11009-006-9014-2
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    References listed on IDEAS

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    1. Picard, Philippe & Lefèvre, Claude, 2003. "On the first meeting or crossing of two independent trajectories for some counting processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 217-242, April.
    2. Ignatov, Zvetan G. & Kaishev, Vladimir K. & Krachunov, Rossen S., 2001. "An improved finite-time ruin probability formula and its Mathematica implementation," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 375-386, December.
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