Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/257911 
Year of Publication: 
2019
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 7 [Issue:] 3 [Article No.:] 73 [Publisher:] MDPI [Place:] Basel [Year:] 2019 [Pages:] 1-11
Publisher: 
MDPI, Basel
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.
Subjects: 
barrier strategies
log-convexity
optimal dividends
Parisian ruin
spectrally negative Lévy processes
stochastic control
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
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