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On the Parisian ruin of the dual Lévy risk model

Part of: Mathematical economics

Published online by Cambridge University Press:  30 November 2017

Chen Yang ,
Kristian P. Sendova  and
Zhong Li
Chen Yang*
Affiliation:
Wuhan University
Kristian P. Sendova*
Affiliation:
University of Western Ontario
Zhong Li*
Affiliation:
University of International Business and Economics
*
* Postal address: Economics and Management School of Wuhan University, Wuhan, Hubei, 430072, P. R. China. Email address: cyang244@whu.edu.cn
** Postal address: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario, N6A 5B7, Canada. Email address: ksendova@stats.uwo.ca
*** Postal address: School of Insurance and Economics, University of International Business and Economics, Beijing, 100029, P. R. China. Email address: 02437@uibe.edu.cn
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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.

Keywords

Parisian ruinLévy processdual risk modelGerber–Shiu function

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 91B70: Stochastic models
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 4 , December 2017 , pp. 1193 - 1212
Copyright
Copyright © Applied Probability Trust 2017 

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