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

被引：3

作者：

Li, Shuanming ^{[1
]}

Lu, Yi ^{[2
]}

Jin, Can ^{[1
]}

机构：

[1] Univ Melbourne, Dept Econ, Ctr Actuarial Studies, Melbourne, Vic, Australia

[2] Simon Fraser Univ, Dept Stat & Actuarial Sci, 8888 Univ Dr, Burnaby, BC V5A 1S6, Canada

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2016年 / 18卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Classical risk model; Two-sided first-exit time; Two-sided smooth exit-recovery time; Number of claims; Doubly-killed scale function; LEVY PROCESSES; TIMES; SURPLUS; RUIN;

D O I：

10.1007/s11009-015-9453-8

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：747 / 764

页数：18

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