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Optimality of threshold strategies for spectrally negative Levy processes and a positive terminal value at creeping ruin

This paper investigates a dividend optimization problem with a positive creeping-associated terminal value at ruin for spectrally negative Levy processes. We consider an insurance company whose surplus process evolves according to a spectrally negative Levy process with a Gaussian part and a finite Levy 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.