Optimality of Hybrid Continuous and Periodic Barrier Strategies in the Dual Model
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Avanzi et al. (ASTIN Bull 46(3): 709–746, 2016) recently studied an optimal dividend problem where dividends are paid both periodically and continuously with different transaction costs. In the Brownian model with Poissonian periodic dividend payment opportunities, they showed that the optimal strategy is either of the pure-continuous, pure-periodic, or hybrid-barrier type. In this paper, we generalize the results of their previous study to the dual (spectrally positive Lévy) model. The optimal strategy is again of the hybrid-barrier type and can be concisely expressed using the scale function. These results are confirmed through a sequence of numerical experiments.
KeywordsDividends Lévy processes Periodic strategies Scale functions Dual model
Mathematics Subject Classification60G51 93E20 91B30
- 12.Kuznetsov, A., Kyprianou, A.E., Rivero, V.: Lévy Matters II, Springer Lecture Notes in Mathematics. The theory of scale functions for spectrally negative Lévy processes. Springer, Berlin (2013)Google Scholar
- 16.Pérez, J.L., Yamazaki, K.: Mixed periodic-classical barrier strategies for Lévy risk process (2016). arXiv:1609.01671
- 17.Pérez, J.L., Yamazaki, K.: Hybrid continuous and periodic barrier strategies in the dual model: optimality and fluctuation identities (2016). arXiv:1612.02444