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A temporal approach to the Parisian risk model

Part of: Stochastic processes

Published online by Cambridge University Press:  28 March 2018

Bin Li ,
Gordon E. Willmot  and
Jeff T. Y. Wong
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.
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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).

Keywords

Parisian ruinPoisson observationinsurance risk modelspectrally negative Lévy process

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60G51: Processes with independent increments; L'evy processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 302 - 317
Copyright
Copyright © Applied Probability Trust 2018 

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