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Optimality of multi-refraction control strategies in the dual model

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  • Czarna, Irmina
  • Pérez, José-Luis
  • Yamazaki, Kazutoshi

Abstract

We consider the multi-refraction strategies in two equivalent versions of the optimal dividend problem in the dual (spectrally positive Lévy) model. The first problem is a variant of the bail-out case where both dividend payments and capital injections must be absolutely continuous with respect to the Lebesgue measure. The second is an extension of Avanzi et al. (2017) where a strategy is a combination of two absolutely continuous dividend payments with different upper bounds and different transaction costs. In both problems, it is shown to be optimal to refract the process at two thresholds, with the optimally controlled process being the multi-refracted Lévy process recently studied by Czarna et al. (0000). The optimal strategy and the value function are succinctly written in terms of a version of the scale function. Numerical results are also given.

Suggested Citation

  • Czarna, Irmina & Pérez, José-Luis & Yamazaki, Kazutoshi, 2018. "Optimality of multi-refraction control strategies in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 148-160.
    • Handle: RePEc:eee:insuma:v:83:y:2018:i:c:p:148-160
    DOI: 10.1016/j.insmatheco.2018.09.008
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    References listed on IDEAS

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    More about this item

    Keywords

    Dividends; Capital injection; Lévy processes; Scale functions; Dual model;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy

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