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On the Parisian ruin of the dual Lévy risk model

Published online by Cambridge University Press:  30 November 2017

Chen Yang
Affiliation:
Wuhan University
Kristian P. Sendova
Affiliation:
University of Western Ontario
Zhong Li
Affiliation:
University of International Business and Economics
Corresponding

Abstract

In this paper we investigate the Parisian ruin problem of the general dual Lévy risk model. Unlike the usual concept of ultimate ruin, allowing the surplus level to be negative within a prespecified period indicates that the deficit at Parisian ruin is not necessarily equal to zero. Hence, we consider a Gerber–Shiu type expected discounted penalty function at the Parisian ruin and obtain an explicit expression for this function under the dual Lévy risk model. As particular cases, we calculate the Parisian ruin probability and the expected discounted kth moments of the deficit at the Parisian ruin for the compound Poisson dual risk model and a drift-diffusion model. Numerical examples are given to illustrate the behavior of Parisian ruin and the expected discounted deficit at Parisian ruin.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2017 

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