scholarly journals Minimizing the Discounted Probability of Exponential Parisian Ruin via Reinsurance

2020 ◽  
Vol 58 (2) ◽  
pp. 937-964
Author(s):  
Xiaoqing Liang ◽  
Virginia R. Young
Keyword(s):  
Parisian Ruin

scholarly journals A VaR-Type Risk Measure Derived from Cumulative Parisian Ruin for the Classical Risk Model

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 85 ◽  
Author(s):  
Mohamed Lkabous ◽  
Jean-François Renaud
Keyword(s):  
Risk Model ◽  
Risk Measures ◽  
Risk Measure ◽  
Short Paper ◽  
Classical Risk Model ◽  
Parisian Ruin ◽  
The Classical Risk Model

In this short paper, we study a VaR-type risk measure introduced by Guérin and Renaud and which is based on cumulative Parisian ruin. We derive some properties of this risk measure and we compare it to the risk measures of Trufin et al. and Loisel and Trufin.

scholarly journals Gerber–Shiu distribution at Parisian ruin for Lévy insurance risk processes

2016 ◽  
Vol 53 (2) ◽  
pp. 572-584 ◽  
Author(s):  
Erik J. Baurdoux ◽  
Juan Carlos Pardo ◽  
José Luis Pérez ◽  
Jean-François Renaud
Keyword(s):  
Risk Process ◽  
Levy Processes ◽  
Insurance Company ◽  
Excursion Theory ◽  
Insurance Risk ◽  
Scale Functions ◽  
Surplus Process ◽  
Parisian Ruin ◽  
Risk Processes ◽  
Spectrally Negative Lévy Processes

Abstract Inspired by the works of Landriault et al. (2011), (2014), we study the Gerber–Shiu distribution at Parisian ruin with exponential implementation delays for a spectrally negative Lévy insurance risk process. To be more specific, we study the so-called Gerber–Shiu distribution for a ruin model where at each time the surplus process goes negative, an independent exponential clock is started. If the clock rings before the surplus becomes positive again then the insurance company is ruined. Our methodology uses excursion theory for spectrally negative Lévy processes and relies on the theory of so-called scale functions. In particular, we extend the recent results of Landriault et al. (2011), (2014).

Parisian Ruin with Erlang Delay and a Lower Bankruptcy Barrier

2019 ◽  
Vol 22 (1) ◽  
pp. 101-134 ◽  
Author(s):  
Esther Frostig ◽  
Adva Keren-Pinhasik
Keyword(s):  
Parisian Ruin

scholarly journals On the distribution of cumulative Parisian ruin

2017 ◽  
Vol 73 ◽  
pp. 116-123 ◽  
Author(s):  
Hélène Guérin ◽  
Jean-François Renaud
Keyword(s):  
Parisian Ruin

scholarly journals Parisian ruin of self-similar Gaussian risk processes

2015 ◽  
Vol 52 (3) ◽  
pp. 688-702 ◽  
Author(s):  
Krzysztof Dębicki ◽  
Enkelejd Hashorva ◽  
Lanpeng Ji
Keyword(s):  
Normal Approximation ◽  
Asymptotic Relation ◽  
Exact Asymptotics ◽  
Ruin Time ◽  
Self Similar ◽  
Parisian Ruin ◽  
Risk Processes

In this paper we derive the exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes. Additionally, we obtain the normal approximation of the Parisian ruin time and derive an asymptotic relation between the Parisian and the classical ruin times.

scholarly journals Parisian ruin for a refracted Lévy process

2017 ◽  
Vol 74 ◽  
pp. 153-163 ◽  
Author(s):  
Mohamed Amine Lkabous ◽  
Irmina Czarna ◽  
Jean-François Renaud
Keyword(s):  
Lévy Process ◽  
Levy Process ◽  
Parisian Ruin

Parisian ruin in the dual model with applications to the G/M/1 queue

2017 ◽  
Vol 86 (3-4) ◽  
pp. 261-275 ◽  
Author(s):  
Esther Frostig ◽  
Adva Keren–Pinhasik
Keyword(s):  
Dual Model ◽  
Parisian Ruin
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