An Insurance Risk Model with Parisian Implementation Delays

被引:68
作者
Landriault, David [1 ]
Renaud, Jean-Francois [2 ]
Zhou, Xiaowen [3 ]
机构
[1] Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON N2L 3G1, Canada
[2] Univ Quebec Montreal UQAM, Dept Math, Montreal, PQ H2X 3Y7, Canada
[3] Concordia Univ, Dept Math & Stat, Montreal, PQ H3G 1M8, Canada
关键词
Insurance risk theory; Implementation delays; Parisian ruin; Levy processes; Scale functions;
D O I
10.1007/s11009-012-9317-4
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 consider a similar variant of the event ruin for a Levy insurance risk process as in Czarna and Palmowski (J Appl Probab 48(4):984-1002, 2011) and Loeffen et al. (to appear, 2011) when the surplus process is allowed to spend time under a pre-specified default level before ruin is recognized. In these two articles, the ruin probability is examined when deterministic implementation delays are allowed. In this paper, we propose to capitalize on the idea of randomization and thus assume these delays are of a mixed Erlang nature. Together with the analytical interest of this problem, we will show through the development of new methodological tools that these stochastic delays lead to more explicit and computable results for various ruin-related quantities than their deterministic counterparts. Using the modern language of scale functions, we study the Laplace transform of this so-called Parisian time to ruin in an insurance risk model driven by a spectrally negative Levy process of bounded variation. In the process, a generalization of the two-sided exit problem for this class of processes is further obtained.
引用
收藏
页码:583 / 607
页数:25
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