scholarly journals Occupation Times of Intervals Until Last Passage Times for Spectrally Negative Lévy Processes

2017 ◽  
Vol 31 (4) ◽  
pp. 2194-2215 ◽  
Author(s):  
Chunhao Cai ◽  
Bo Li
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Occupation Times ◽  
Last Passage Times ◽  
Spectrally Negative Lévy Processes ◽  
Passage Times

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 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

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.

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