Optimal Dividend Policies with Random Profitability

38 Pages Posted: 10 Jan 2018

See all articles by Max Reppen

Max Reppen

ETH Zürich

Jean-Charles Rochet

Swiss Finance Institute; University of Geneva - Geneva Finance Research Institute (GFRI); University of Zurich - Swiss Banking Institute (ISB)

H. Mete Soner

ETH Zürich - Department of Mathematics

Date Written: May 31, 2017

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 uniqueness of the solution to the Hamilton–Jacobi–Bellman equation, and study its qualitative properties both analytically and numerically. The value function is thus 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 gambling for resurrection.

Suggested Citation

Reppen, Max and Rochet, Jean-Charles and Soner, H. Mete, Optimal Dividend Policies with Random Profitability (May 31, 2017). Swiss Finance Institute Research Paper No. 17-46, Available at SSRN: https://ssrn.com/abstract=3099015 or http://dx.doi.org/10.2139/ssrn.3099015

Max Reppen

ETH Zürich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

Jean-Charles Rochet

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva - Geneva Finance Research Institute (GFRI) ( email )

40 Boulevard du Pont d'Arve
Geneva 4, Geneva 1211
Switzerland

University of Zurich - Swiss Banking Institute (ISB) ( email )

Plattenstrasse 14
CH-8032 Zurich, Zurich 8032
Switzerland

H. Mete Soner (Contact Author)

ETH Zürich - Department of Mathematics ( email )

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

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