On the Bail-Out Optimal Dividend Problem

José Luis Pérez, Kazutoshi Yamazaki, Xiang Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)


This paper studies the optimal dividend problem with capital injection under the constraint that the cumulative dividend strategy is absolutely continuous. We consider an open problem of the general spectrally negative case and derive the optimal solution explicitly using the fluctuation identities of the refracted–reflected Lévy process. The optimal strategy as well as the value function is concisely written in terms of the scale function. Numerical results are also provided to confirm the analytical conclusions.

Original languageEnglish
Pages (from-to)553-568
Number of pages16
JournalJournal of Optimization Theory and Applications
Issue number2
Publication statusPublished - 1 Nov 2018


  • Bail-out dividend problem
  • Refracted–reflected Lévy processes
  • Scale functions
  • Stochastic control

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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