Journal article
Number of Jumps in Two-Sided First-Exit Problems for a Compound Poisson Process
S Li, Y Lu, C Jin
Methodology and Computing in Applied Probability | Published : 2016
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.
Grants
Awarded by Natural Science and Engineering Research Council (NSERC) of Canada
Funding Acknowledgements
This research for Dr. Yi Lu was partially supported by the Department of Economics, The University of Melbourne, and partially supported by the Natural Science and Engineering Research Council (NSERC) of Canada (grant number RGPIN06148).