Optimality of Threshold Strategies for Spectrally Negative Lévy Processes and a Positive Terminal Value at Creeping Ruin

AbstractThis article investigates a dividend optimization problem with a positive creeping-associated terminal value at ruin for spectrally negative Lévy processes. We consider an insurance company whose surplus process evolves according to a spectrally negative Lévy process with a Gaussian part and a finite Lévy measure. Its objective function relates to dividend payments until ruin and a creeping-associated terminal value at ruin. The positive creeping-associated terminal value represents the salvage value or the creeping reward when creeping happens. Owing to formulas from fluctuation theory, the objective considered is represented explicitly. Under certain restrictions on the terminal value and the surplus process, we show that the threshold strategy should be the optimal one over an admissible class with bounded dividend rates. ACKNOWLEDGMENTI am truly grateful to the two anonymous referees for giving their valuable guiding comments on this work.Disclosure StatementNo potential conflict of interest was reported by the author.