Optimal dividend policies with random profitability

A. Max Reppen, Jean Charles Rochet, H. Mete Soner

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We study an optimal dividend problem under a bankruptcy constraint. Firms face a trade-off between potential bankruptcy and extraction of profits. In contrast to previous works, general cash flow drifts, including Ornstein–Uhlenbeck and CIR processes, are considered. We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as comparison between discontinuous sub- and supersolutions of the Hamilton–Jacobi–Bellman equation, and we provide an efficient and convergent numerical scheme for finding the solution. The value function is given by a nonlinear partial differential equation (PDE) with a gradient constraint from below in one direction. We find that the optimal strategy is both a barrier and a band strategy and that it includes voluntary liquidation in parts of the state space. Finally, we present and numerically study extensions of the model, including equity issuance and gambling for resurrection.

Original languageEnglish (US)
Pages (from-to)228-259
Number of pages32
JournalMathematical Finance
Issue number1
StatePublished - Jan 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Accounting
  • Social Sciences (miscellaneous)
  • Finance
  • Economics and Econometrics
  • Applied Mathematics


  • barrier strategy
  • dividend problem
  • singular control
  • viscosity solutions


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