Number of Jumps in Two-Sided First-Exit Problems for a Compound Poisson Process

Shuanming Li, Yi Lu () and Can Jin
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Shuanming Li: The University of Melbourne
Yi Lu: Simon Fraser University
Can Jin: The University of Melbourne

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 3, 747-764

Abstract: Abstract In this paper, we study the joint Laplace transform and probability generating functions of two pairs of random variables: (1) the two-sided first-exit time and the number of claims by this time; (2) the two-sided smooth exit-recovery time and its associated number of claims. The joint transforms are expressed in terms of the so-called doubly-killed scale function that is defined in this paper. We also find explicit expressions for the joint density function of the two-sided first-exit time and the number of claims by this time. Numerical examples are presented for exponential claims.

Keywords: Classical risk model; Two-sided first-exit time; Two-sided smooth exit-recovery time; Number of claims; Doubly-killed scale function; 91B30; 37A50 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11009-015-9453-8

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