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

TL;DR

This paper proves that threshold strategies are optimal for dividend payout problems involving spectrally negative Levy processes with a positive terminal value at creeping ruin, using explicit fluctuation theory formulas.

Contribution

It establishes the optimality of threshold strategies in a dividend optimization model with a positive terminal value at creeping ruin for spectrally negative Levy processes.

Findings

Threshold strategies are optimal under certain conditions.

Explicit formulas from fluctuation theory facilitate analysis.

Optimality holds within a class of bounded dividend rates.

Abstract

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.