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Parisian ruin of self-similar Gaussian risk processes

Part of: Stochastic processes

Published online by Cambridge University Press:  30 March 2016

Krzysztof Dębicki ,
Enkelejd Hashorva  and
Lanpeng Ji
Krzysztof Dębicki*
Affiliation:
University of Wrocław
Enkelejd Hashorva*
Affiliation:
University of Lausanne
Lanpeng Ji*
Affiliation:
University of Lausanne
*
∗ Postal address: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland.
∗∗ Postal address: University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland.
∗∗ Postal address: University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland.
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Abstract

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In this paper we derive the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes. Additionally, we obtain the normal approximation of the Parisian ruin time and derive an asymptotic relation between the Parisian and the classical ruin times.

Keywords

Parisian ruin timeParisian ruin probabilityself-similar Gaussian processfractional Brownian motionnormal approximationgeneralized Pickands' constant

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G70: Extreme value theory; extremal processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 688 - 702
Copyright
Copyright © 2015 by the Applied Probability Trust 

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