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

Jean-François Renaud
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Jean-François Renaud: Département de mathématiques, Université du Québec à Montréal (UQAM), Montréal, QC H2X 3Y7, Canada

Risks, 2019, vol. 7, issue 3, 1-11

Abstract: 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.

Keywords: stochastic control; spectrally negative Lévy processes; optimal dividends; Parisian ruin; log-convexity; barrier strategies (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:7:y:2019:i:3:p:73-:d:245263

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