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On first and last ruin times of Gaussian processes

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  • Hüsler, Jürg
  • Zhang, Yueming

Abstract

Considering centered Gaussian processes X(t) with a trend -ct[beta] and variance V2(t), we are interested in the asymptotic distributions of the first ruin time and the last ruin time as well as their joint asymptotic distribution as the initial capital u-->[infinity]. Our results show that the conditional distribution of the last ruin time, conditioned on ruin occurring, is a normal distribution and the conditional joint limit distribution is a difference of two standard normal distributions.

Suggested Citation

  • Hüsler, Jürg & Zhang, Yueming, 2008. "On first and last ruin times of Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1230-1235, August.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:10:p:1230-1235
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    References listed on IDEAS

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    7. Chiu, S. N. & Yin, C. C., 2003. "The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 59-66, August.
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