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December 2014 On the time spent in the red by a refracted Lévy risk process
Jean-François Renaud
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J. Appl. Probab. 51(4): 1171-1188 (December 2014).

Abstract

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.

Citation

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Jean-François Renaud. "On the time spent in the red by a refracted Lévy risk process." J. Appl. Probab. 51 (4) 1171 - 1188, December 2014.

Information

Published: December 2014
First available in Project Euclid: 20 January 2015

zbMATH: 1307.90196
MathSciNet: MR3301295

Subjects:
Primary: 60G51
Secondary: 91B30

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 4 • December 2014
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