Optimal dividend policies with random profitability

TL;DR

This paper investigates optimal dividend policies under bankruptcy risk with general cash flow models, providing theoretical proofs, numerical schemes, and characterizing strategies as barrier and band types with extensions.

Contribution

It introduces a comprehensive model with general cash flow processes, proves the continuity of the value function, and characterizes optimal strategies including liquidation, with extensions like equity issuance.

Findings

Optimal strategies are barrier and band strategies.

The value function satisfies a nonlinear PDE with a gradient constraint.

Extensions include models with equity issuance and credit lines.

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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