A limit theorem for the time of ruin in a Gaussian ruin problem

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Huesler, Juerg¹  Piterbarg, Vladimir² 

[1] Univ Bern, Dept Math Stat, CH-3095 Bern, Switzerland

[2] Moscow MV Lomonosov State Univ, Moscow, Russia

关键词: Gaussian process;    Nonstationary;    Locally stationary;    Ruin;    Ruin time;    Asymptotic behavior;    Limit distributions;   

DOI  :  10.1016/j.spa.2007.11.006

来源: Elsevier

【 摘 要 】

For certain Gaussian processes X(t) with trend -ct(beta) and variance V(2)(t), the ruin time is analyzed where the ruin time is defined as the first time point t such that X(t) - ct(beta) >= u. The ruin time is of interest in finance and actuarial subjects. But the ruin time is also of interest in other applications, e.g. in telecommunications where it indicates the first time of an overflow. We derive the asymptotic distribution of the ruin time as u -> infinity showing that the limiting distribution depends on the parameters beta, V(t) and the correlation function of X(t). (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free