Number of Jumps in Two-Sided First-Exit Problems for a Compound Poisson Process
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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.
KeywordsClassical risk model Two-sided first-exit time Two-sided smooth exit-recovery time Number of claims Doubly-killed scale function
Mathematical Subject Classifications (2010)91B30 37A50
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