scholarly journals On the Time Spent in the Red by a Refracted Lévy Risk Process

2014 ◽  
Vol 51 (4) ◽  
pp. 1171-1188 ◽  
Author(s):  
Jean-François Renaud
Keyword(s):  
Lévy Processes ◽  
Risk Process ◽  
Levy Processes ◽  
Occupation Times ◽  
Premium Rate ◽  
Probability Of Bankruptcy ◽  
Parisian Ruin ◽  
Spectrally Negative Lévy Processes

In this paper we introduce an insurance ruin model with an adaptive premium rate, henceforth referred to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regular level when the wealth process recovers. The analysis is focused mainly on the time a refracted Lévy risk process spends in the red zone (analogous to the duration of the negative surplus). Building on results from [11] and [16], we identify the distribution of various functionals related to occupation times of refracted spectrally negative Lévy processes. For example, these results are used to compute both the probability of bankruptcy and the probability of Parisian ruin in this model with restructuring.

scholarly journals On the Time Spent in the Red by a Refracted Lévy Risk Process

2014 ◽  
Vol 51 (04) ◽  
pp. 1171-1188 ◽  
Author(s):  
Jean-François Renaud
Keyword(s):  
Lévy Processes ◽  
Risk Process ◽  
Levy Processes ◽  
Occupation Times ◽  
Premium Rate ◽  
Probability Of Bankruptcy ◽  
Parisian Ruin ◽  
Spectrally Negative Lévy Processes

In this paper we introduce an insurance ruin model with an adaptive premium rate, henceforth referred to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regular level when the wealth process recovers. The analysis is focused mainly on the time a refracted Lévy risk process spends in the red zone (analogous to the duration of the negative surplus). Building on results from [11] and [16], we identify the distribution of various functionals related to occupation times of refracted spectrally negative Lévy processes. For example, these results are used to compute both the probability of bankruptcy and the probability of Parisian ruin in this model with restructuring.

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).

Spectrally negative Lévy processes with applications in risk theory

2001 ◽  
Vol 33 (1) ◽  
pp. 281-291 ◽  
Author(s):  
Hailiang Yang ◽  
Lianzeng Zhang
Keyword(s):  
Lévy Processes ◽  
Compound Poisson Process ◽  
Risk Process ◽  
Levy Processes ◽  
Point Of View ◽  
Ruin Time ◽  
Classical Risk Process ◽  
Risk Processes ◽  
First Time ◽  
Spectrally Negative Lévy Processes

In this paper, results on spectrally negative Lévy processes are used to study the ruin probability under some risk processes. These processes include the compound Poisson process and the gamma process, both perturbed by diffusion. In addition, the first time the risk process hits a given level is also studied. In the case of classical risk process, the joint distribution of the ruin time and the first recovery time is obtained. Some results in this paper have appeared before (e.g., Dufresne and Gerber (1991), Gerber (1990), dos Reis (1993)). We revisit them from the Lévy process theory's point of view and in a unified and simple way.

scholarly journals Parisian ruin probability for spectrally negative Lévy processes

Bernoulli ◽  
2013 ◽  
Vol 19 (2) ◽  
pp. 599-609 ◽  
Author(s):  
Ronnie Loeffen ◽  
Irmina Czarna ◽  
Zbigniew Palmowski
Keyword(s):  
Ruin Probability ◽  
Lévy Processes ◽  
Levy Processes ◽  
Parisian Ruin ◽  
Spectrally Negative Lévy Processes

scholarly journals Occupation times of spectrally negative Lévy processes with applications

2011 ◽  
Vol 121 (11) ◽  
pp. 2629-2641 ◽  
Author(s):  
David Landriault ◽  
Jean-François Renaud ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Occupation Times ◽  
Spectrally Negative Lévy Processes
Sign in / Sign up

Export Citation Format

Share Document