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Optimality of Hybrid Continuous and Periodic Barrier Strategies in the Dual Model

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Abstract

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.

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Authors and Affiliations

  1. Department of Probability and Statistics, Centro de Investigación en Matemáticas, A.C. Calle Jalisco s/n., C.P. 36240, Guanajuato, Mexico

    José-Luis Pérez

  2. Department of Mathematics, Faculty of Engineering Science, Kansai University, 3-3-35 Yamate-cho, Suita-shi, Osaka, 564-8680, Japan

    Kazutoshi Yamazaki

Authors
  1. José-Luis Pérez
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  2. Kazutoshi Yamazaki
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Corresponding author

Correspondence to Kazutoshi Yamazaki.

Additional information

This version: January 27, 2018. J. L. Pérez is supported by CONACYT, Project No. 241195. K. Yamazaki is supported by MEXT KAKENHI Grant No. 26800092 and 17K05377.

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Pérez, JL., Yamazaki, K. Optimality of Hybrid Continuous and Periodic Barrier Strategies in the Dual Model. Appl Math Optim 82, 105–133 (2020). https://doi.org/10.1007/s00245-018-9494-9

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