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

页码：29 / 51

页数：23

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