Optimal Dividend Policies with Random Profitability

32 Pages Posted: 29 May 2020

See all articles by A. Max Reppen

A. Max Reppen

Princeton University

Jean‐Charles Rochet

University of Geneva

H. Mete Soner

ETH Zürich - Department of Mathematics

Date Written: January 2020

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 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.

Keywords: barrier strategy, dividend problem, singular control, viscosity solutions

Suggested Citation

Reppen, A. Max and Rochet, Jean‐Charles and Soner, H. Mete, Optimal Dividend Policies with Random Profitability (January 2020). Mathematical Finance, Vol. 30, Issue 1, pp. 228-259, 2020, Available at SSRN: https://ssrn.com/abstract=3613905 or http://dx.doi.org/10.1111/mafi.12223

A. Max Reppen (Contact Author)

Princeton University

22 Chambers Street
Princeton, NJ 08544-0708
United States

Jean‐Charles Rochet

University of Geneva

102 Bd Carl-Vogt
Genève, CH - 1205
Switzerland

H. Mete Soner

ETH Zürich - Department of Mathematics ( email )

R¨amistrasse 101
Raemistr. 101
Z¨urich, 8092
Switzerland

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