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A temporal approach to the Parisian risk model

Published online by Cambridge University Press:  28 March 2018

Bin Li*
Affiliation:
University of Waterloo
Gordon E. Willmot*
Affiliation:
University of Waterloo
Jeff T. Y. Wong*
Affiliation:
University of Waterloo
*
* Postal address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada.
* Postal address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada.
* Postal address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada.

Abstract

In this paper we propose a new approach to study the Parisian ruin problem for spectrally negative Lévy processes. Since our approach is based on a hybrid observation scheme switching between discrete and continuous observations, we call it a temporal approach as opposed to the spatial approximation approach in the literature. Our approach leads to a unified proof for the underlying processes with bounded or unbounded variation paths, and our result generalizes Loeffen et al. (2013).

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2018 

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