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Optimal dividends and capital injection: A general Lévy model with extensions to regime-switching models

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  • Mata López, Dante
  • Noba, Kei
  • Pérez, José-Luis
  • Yamazaki, Kazutoshi

Abstract

This paper studies a general Lévy process model of the bail-out optimal dividend problem with an exponential time horizon, and further extends it to the regime-switching model. We first show the optimality of a double barrier strategy in the single-regime setting with a concave terminal payoff function. This is then applied to show the optimality of a Markov-modulated double barrier strategy in the regime-switching model via contraction mapping arguments. We solve these for a general Lévy model with both positive and negative jumps, greatly generalizing the existing results on spectrally one-sided models.

Suggested Citation

  • Mata López, Dante & Noba, Kei & Pérez, José-Luis & Yamazaki, Kazutoshi, 2024. "Optimal dividends and capital injection: A general Lévy model with extensions to regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 210-225.
    • Handle: RePEc:eee:insuma:v:119:y:2024:i:c:p:210-225
    DOI: 10.1016/j.insmatheco.2024.08.007
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