# Extremes of γ-reflected Gaussian processes with stationary increments

## Details

Serval ID
serval:BIB_113D6DBB556B
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Extremes of γ-reflected Gaussian processes with stationary increments
Journal
ESAIM: Probability and Statistics
ISSN
1292-8100
1262-3318
Publication state
Published
Issued date
2017
Peer-reviewed
Oui
Volume
21
Pages
495-535
Language
english
Abstract
For a given centered Gaussian process with stationary increments $\{X(t), t\geq 0\}$ and $c>0$, let $$W_\gamma(t)=X(t)-ct-\gamma\inf_{0\leq s\leq t}\left(X(s)-cs\right), \quad t\geq 0$$ denote the $\gamma$-reflected process, where $\gamma\in (0,1)$. This process is introduced in the context of risk theory to model surplus process that include tax payments of loss-carry forward type.In this contribution we derive asymptotic approximations of both the ruin probability and the joint distribution of first and last passage times given that ruin occurs. We apply our findings to the cases with $X$ being the multiplex fractional Brownian motion and the integrated Gaussian processes. As a by-product we derive an extension of Piterbarg inequality \KD{for} threshold-dependent random fields.

Keywords
Statistics and Probability, Statistics and Probability, Statistics and Probability
Create date
11/11/2017 13:26
Last modification date
21/08/2019 6:17
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