Optimal dividends in the dual model under transaction costs

Abstract

We analyze the optimal dividend payment problem in the dual model under constant transaction costs. We show, for a general spectrally positive Lévy process, an optimal strategy is given by a $(c_1,c_2)$-policy that brings the surplus process down to $c_1$ whenever it reaches or exceeds $c_2$ for some $0\le c_1<c_2$. The value function is succinctly expressed in terms of the scale function. A series of numerical examples are provided to confirm the analytical results and to demonstrate the convergence to the no-transaction cost case, which was recently solved by Bayraktar et al. (2013).

Final version. To appear in Insurance: Mathematics and Economics. Key words: dual model; dividends; impulse control; spectrally positive Levy processes; scale functions

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• On the optimal dividend problem for a spectrally negative Lévy process
• Inventory Control for Spectrally Positive Levy Demand Processes