A unified approach to ruin probabilities with delays for spectrally negative Lévy processes

Lkabous, Mohamed Amine and Renaud, Jean François (2019) A unified approach to ruin probabilities with delays for spectrally negative Lévy processes. Scandinavian Actuarial Journal, 2019 (8), 711-728. (doi:10.1080/03461238.2019.1598890).

Record type: Article

Abstract

In this paper, we unify two popular approaches for the definition of actuarial ruin with implementation delays, also known as Parisian ruin. Our new definition of ruin includes both deterministic delays and exponentially distributed delays: ruin is declared the first time an excursion in the red zone lasts longer than an implementation delay with a deterministic and a stochastic component. For this Parisian ruin with mixed delays, we identify the joint distribution of the time of ruin and the deficit at ruin, therefore providing generalizations of many results previously obtained, such as in Baurdoux et al. (2016) and Loeffen et al. (in press) for the case of an exponential delay and that of a deterministic delay, respectively.

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More information

Accepted/In Press date: 20 March 2019

e-pub ahead of print date: 27 March 2019

Published date: 14 September 2019

Additional Information: Funding Information: in support of this work was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC). M. A. Lkabous thanks the Institut des sciences mathématiques (ISM) and the Faculté des sciences at UQAM for their financial support (PhD scholarships). We would like to thank an anonymous referee for her/his helpful suggestions that greatly improved the paper. Publisher Copyright: © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

Keywords: Lévy insurance risk processes, Parisian ruin, Ruin with delays