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We analyze the optimal dividend payment problem in the dual model underconstant transaction costs. We show, for a general spectrally positive L\'{e}vyprocess, an optimal strategy is given by a $(c_1,c_2)$-policy that brings thesurplus process down to $c_1$ whenever it reaches or exceeds $c_2$ for some $0\leq c_1 < c_2$. The value function is succinctly expressed in terms of thescale function. A series of numerical examples are provided to confirm theanalytical results and to demonstrate the convergence to the no-transactioncost case, which was recently solved by Bayraktar et al. (2013).

Optimal dividends in the dual model under transaction costs