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

Part of: Stochastic processes Mathematical economics

Published online by Cambridge University Press:  30 January 2018

Jean-François Renaud
Jean-François Renaud*
Affiliation:
UQAM
*
∗ Postal address: Département de Mathématiques, Université du Québec à Montréal (UQAM), 201 Av. Président-Kennedy, Montréal, Québec, H2X 3Y7, Canada. Email address: [email protected]
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Abstract

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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.

Keywords

Spectrally negative Lévy processrefractionoccupation timebankruptcyParisian ruin

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 91B30: Risk theory, insurance
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 1171 - 1188
Copyright
© Applied Probability Trust 

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