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Optimal dividend policies with random profitability

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  • Max Reppen
  • Jean-Charles Rochet
  • H. Mete Soner

Abstract

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 the 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 PDE with a gradient constraint from below in one dimension. 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 credit lines.

Suggested Citation

  • Max Reppen & Jean-Charles Rochet & H. Mete Soner, 2017. "Optimal dividend policies with random profitability," Papers 1706.01813, arXiv.org, revised Mar 2018.
  • Handle: RePEc:arx:papers:1706.01813
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    Cited by:

    1. Ferrari, Giorgio & Schuhmann, Patrick & Zhu, Shihao, 2021. "Optimal Dividends under Markov-Modulated Bankruptcy Level," Center for Mathematical Economics Working Papers 657, Center for Mathematical Economics, Bielefeld University.
    2. Amlys Syahputra Silalahi & Khaira Amalia Fachrudin & Aryanti Sariartha Sianipar & Kharisya Ayu Effendi, 2021. "Analysis of the Bank Specific Factors, Macroeconomics and Oil Price on Dividend Policy," International Journal of Energy Economics and Policy, Econjournals, vol. 11(2), pages 165-171.
    3. Giorgio Ferrari & Patrick Schuhmann & Shihao Zhu, 2021. "Optimal Dividends under Markov-Modulated Bankruptcy Level," Papers 2111.03724, arXiv.org.
    4. Stefan Kremsner & Alexander Steinicke & Michaela Szölgyenyi, 2020. "A Deep Neural Network Algorithm for Semilinear Elliptic PDEs with Applications in Insurance Mathematics," Risks, MDPI, vol. 8(4), pages 1-18, December.
    5. Bandini, Elena & de Angelis, Tiziano & Ferrari, Giorgio & Gozzi, Fausto, 2020. "Optimal Dividend Payout under Stochastic Discounting," Center for Mathematical Economics Working Papers 636, Center for Mathematical Economics, Bielefeld University.
    6. Calvia, Alessandro & Ferrari, Giorgio, 2021. "Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control," Center for Mathematical Economics Working Papers 651, Center for Mathematical Economics, Bielefeld University.
    7. Alex S. L. Tse, 2020. "Dividend policy and capital structure of a defaultable firm," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 961-994, July.

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