On the time spent in the red by a refracted L\'evy risk process

In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered 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 process recovers. The analysis is mainly focused on the time a refracted L\'evy risk process spends in the red zone (analogous to the duration of the negative surplus). Building on results from Kyprianou and Loeffen (2010) and Loeffen et al. (2012), we identify the distribution of various functionals related to occupation times of refracted spectrally negative L\'evy processes. For example, these results are used to compute the probability of bankruptcy and the probability of Parisian ruin in this model with restructuring

The distribution of tax payments in a Lévy insurance risk model with a surplus-dependent taxation structure

We study the distribution of tax payments in the model of Kyprianou and Zhou [Kyprianou, A.E., Zhou, X., 2009. General tax structures and the Lévy insurance risk model. J. Appl. Probab. (in press)], that is a Lévy insurance risk model with a surplus-dependent tax rate. More precisely, after a short discussion on the so-called tax identity, we derive a recursive formula for arbitrary moments of the discounted tax payments until ruin and we identify the distribution of the tax payments when there is no force of interest

L’intégration professionnelle des nouveaux immigrants : effet de la connaissance pré-migratoire du français et (ou) de l’anglais

Au Québec, on soumet les nouveaux immigrants à une évaluation serrée du niveau de leurs compétences linguistiques (en français ou en anglais), dans le but de sélectionner des candidats susceptibles de réussir leur établissement socio-économique. Pour des raisons sociales et politiques, on accorde une attention particulière à la connaissance du français à l’arrivée, dans le but de favoriser une meilleure participation au marché du travail. Dans cet article, les auteurs examinent l’effet à moyen et à long terme de la connaissance du français et (ou) de l’anglais sur la performance des nouveaux immigrants sur le marché de l’emploi. Pour les analyses, ils ont recours à une enquête longitudinale sur l’établissement des nouveaux immigrants (ENI), décrivant leurs parcours biographiques. L’ENI présente, sur une période de dix ans, les principaux gestes d’établissement (logement, cours, emploi, etc.) de 429 nouveaux arrivants ayant comme destination la grande région de Montréal. On constate essentiellement que la connaissance pré-migratoire du français et (ou) de l’anglais est un facteur temporaire donnant accès aux emplois qualifiés ou mieux rémunérés, mais qu’elle n’a aucune incidence sur la participation au marché du travail.In Québec, the French and/or English language skills of new immigrants are rigorously assessed in order to select those most likely to become socioeconomically well established. For social and political reasons, particular emphasis is placed on their knowledge of French upon arrival so as to foster their more successful labour market participation. In this article, the authors examine the effect, over the medium and long term, of knowledge of French and/or English on the job market performance of new immigrants. The authors’ analyses are based on a longitudinal survey of the settlement of new immigrants (ENI) that outlines their individual trajectories. The ENI profiles the main settlement actions (housing, education, employment, etc.) of 429 new immigrants to the Greater Montréal area over a ten-year period. The authors’ key finding is that pre-migratory knowledge of French and/or English is a temporary factor that helps immigrants to obtain skilled or better paying jobs, but does not affect their labour market participation

Optimality of a refraction strategy in the optimal dividends problem with absolutely continuous controls subject to Parisian ruin

We consider de Finetti's optimal dividends problem with absolutely continuous strategies in a spectrally negative L\'evy model with Parisian ruin as the termination time. The problem considered is essentially a generalization of both the control problems considered by Kyprianou, Loeffen & P\'erez (2012) and by Renaud (2019). Using the language of scale functions for Parisian fluctuation theory, and under the assumption that the density of the L\'evy measure is completely monotone, we prove that a refraction dividend strategy is optimal and we characterize the optimal threshold. In particular, we study the effect of the rate of Parisian implementation delays on this optimal threshold