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.
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Li, S., Lu, Y. & Jin, C. Number of Jumps in Two-Sided First-Exit Problems for a Compound Poisson Process. Methodol Comput Appl Probab 18, 747–764 (2016). https://doi.org/10.1007/s11009-015-9453-8
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DOI: https://doi.org/10.1007/s11009-015-9453-8
Keywords
- Classical risk model
- Two-sided first-exit time
- Two-sided smooth exit-recovery time
- Number of claims
- Doubly-killed scale function