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arXiv · 1706.01813

Optimal dividend policies with random profitability

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

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Max Reppen, Jean-Charles Rochet, H. Mete Soner. 2018-03-01. Optimal dividend policies with random profitability. https://arxiv.org/abs/1706.01813

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