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Open AccessArticle

De Finetti’s Control Problem with Parisian Ruin for Spectrally Negative Lévy Processes

Département de mathématiques, Université du Québec à Montréal (UQAM), Montréal, QC H2X 3Y7, Canada
Risks 2019, 7(3), 73; https://doi.org/10.3390/risks7030073
Received: 12 June 2019 / Revised: 25 June 2019 / Accepted: 26 June 2019 / Published: 3 July 2019
We consider de Finetti’s stochastic control problem when the (controlled) process is allowed to spend time under the critical level. More precisely, we consider a generalized version of this control problem in a spectrally negative Lévy model with exponential Parisian ruin. We show that, under mild assumptions on the Lévy measure, an optimal strategy is formed by a barrier strategy and that this optimal barrier level is always less than the optimal barrier level when classical ruin is implemented. In addition, we give necessary and sufficient conditions for the barrier strategy at level zero to be optimal. View Full-Text
Keywords: stochastic control; spectrally negative Lévy processes; optimal dividends; Parisian ruin; log-convexity; barrier strategies stochastic control; spectrally negative Lévy processes; optimal dividends; Parisian ruin; log-convexity; barrier strategies
MDPI and ACS Style

Renaud, J.-F. De Finetti’s Control Problem with Parisian Ruin for Spectrally Negative Lévy Processes. Risks 2019, 7, 73.

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