De Finetti's control problem with parisian ruin for spectrally negative Lévy processes

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Risks ; ISSN: 2227-9091 ; Volume: 7 ; Year: 2019 ; Issue: 3 ; Pages: 1-11 ; Basel: MDPI

Classification and Topics

• Classification: Wirtschaft
• Subject: barrier strategies ; log-convexity ; optimal dividends ; Parisian ruin ; spectrally negative Lévy processes ; stochastic control

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Renaud, Jean-François
• Event: Veröffentlichung
• (who): MDPI
• (where): Basel
• (when): 2019

Further information

• DOI: doi:10.3390/risks7030073
• Handle: http://hdl.handle.net/10419/257911
• Last update: 10.03.2025, 11:45 AM CET