Occupation times for spectrally negative Lévy processes on the last exit time

2021 ◽  
pp. 109111
Author(s):  
Yingqiu Li ◽  
Yushao Wei ◽  
Zhaohui Peng
Keyword(s):  
Lévy Processes ◽  
Exit Time ◽  
Levy Processes ◽  
Occupation Times ◽  
Last Exit Time ◽  
Spectrally Negative Lévy Processes

scholarly journals On the last exit times for spectrally negative Lévy processes

2017 ◽  
Vol 54 (2) ◽  
pp. 474-489 ◽  
Author(s):  
Yingqiu Li ◽  
Chuancun Yin ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Exit Time ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Occupation Time ◽  
Exit Times ◽  
New Approach ◽  
Last Exit Time ◽  
Spectrally Negative Lévy Processes

Abstract Using a new approach, for spectrally negative Lévy processes we find joint Laplace transforms involving the last exit time (from a semiinfinite interval), the value of the process at the last exit time, and the associated occupation time, which generalize some previous results.

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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