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 (c1, c2) -policy that brings the surplus process down to c1 whenever it reaches or exceeds c2 for some 0 ≤ c1 < c2. 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).
Bayraktar, E., Kyprianou, A. E., & Yamazaki, K. (2014). Optimal dividends in the dual model under transaction costs. Insurance, Mathematics and Economics, 54(1), 133-143. https://doi.org/10.1016/j.insmatheco.2013.11.007