Number of jumps in two-sided first-exit problems for a compound Poisson process

Shuanming Li, Yi Lu, Can Jin

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

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.
Original languageEnglish
Article number1387-5841
Pages (from-to)747-764
Number of pages18
JournalMethodology and Computing in Applied Probability
Volume18
Issue number3
DOIs
Publication statusPublished - 1 Sep 2016
Externally publishedYes

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Exit Problem
Compound Poisson Process
Jump
First Exit Time
Scale Function
Probability generating function
Density Function
Laplace transform
Recovery
Random variable
Transform
Numerical Examples

Cite this

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Number of jumps in two-sided first-exit problems for a compound Poisson process. / Li, Shuanming; Lu, Yi; Jin, Can.

In: Methodology and Computing in Applied Probability, Vol. 18, No. 3, 1387-5841, 01.09.2016, p. 747-764.

Research output: Contribution to journalArticleResearchpeer-review

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