Martingales and the distribution of the time to ruin

被引：8
|
作者：
Jacobsen, M [1 ]
机构：
[1] Univ Copenhagen, Dept Appl Math & Stat, DK-2100 Copenhagen, Denmark
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2003年 / 107卷 / 01期
关键词：
risk process; probability of ruin; time to ruin; martingales; optional sampling; piecewise deterministic Markov processes;
D O I：
10.1016/S0304-4149(03)00072-3
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：
We determine the ultimate ruin probability and the Laplace transform of the distribution of the time to ruin in the classical risk model, where claims arrive according to a renewal process, with waiting times that are of phase-type, while the claims themselves follow a distribution with a Laplace transform that is a rational function. The main tools are martingales, the optional sampling theorem and results from the theory of piecewise deterministic Markov processes. (C) 2003 Elsevier B.V. All rights reserved.
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页码：29 / 51
页数：23
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