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.
引用
收藏
页码：29 / 51
页数：23
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