Discrete Compound Poisson Process with Curved Boundaries: Polynomial Structures and Recursions |
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Authors: | Claude Lefèvre |
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Institution: | (1) Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, B-1050 Brussels, Belgium |
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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.
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Keywords: | first crossing time compound Poisson process order statistics generalized Appell polynomials generalized Abel– Gontcharoff polynomials recursive methods dam modelling risk theory |
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