## Optimal dividends in the dual model under transaction costs.(English)Zbl 1294.91071

Summary: 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 $$0\leq c_1<c_2$$. 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 E. Bayraktar et al. [Astin Bull. 43, No. 3, 359–372 (2013; Zbl 1283.91192)].

### MSC:

 91B30 Risk theory, insurance (MSC2010) 60G51 Processes with independent increments; Lévy processes 93E20 Optimal stochastic control

Zbl 1283.91192
Full Text:

### References:

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