Discrete dividend payments in continuous time

Jussi Keppo, A. Max Reppen, H. Mete Soner

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are given by discrete time processes. Moreover, between two dividend payments, the structure allows for other types of control; we consider the possibility of equity issuance at any point in time. The value is characterized as the fixed point of an optimal control problem with periodic initial and terminal conditions. We prove the regularity and uniqueness of the corresponding dynamic programming equation and the convergence of an efficient numerical algorithm that we use to study the problem. The model enables us to find the loss caused by infrequent dividend payments. We show that under realistic parameter values, this loss varies from around 1%–24% depending on the state of the system and that using the optimal policy from the continuous problem further increases the loss.

Original languageEnglish (US)
Pages (from-to)895-911
Number of pages17
JournalMathematics of Operations Research
Issue number3
StatePublished - Aug 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Computer Science Applications
  • Management Science and Operations Research


  • Capital structure
  • Equity issuance
  • Impulse control
  • Optimal dividends
  • PDE regularity


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