Article

Optimal dividend policies with random profitability

Jean-Charles Rochet, Max Reppen et Mete Soner

Résumé

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.

Remplace

H. Mete Soner, Max Reppen et Jean-Charles Rochet, « Optimal dividend policies with random profitability », TSE Working Paper, n° 18-886, janvier 2018.

H. Mete Soner, Max Reppen et Jean-Charles Rochet, « Optimal dividend policies with random profitability », IDEI Working Paper, n° 882, janvier 2018.

Référence

Jean-Charles Rochet, Max Reppen et Mete Soner, « Optimal dividend policies with random profitability », Mathematical Finance, vol. 30, n° 1, janvier 2020, p. 228–259.

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Publié dans

Mathematical Finance, vol. 30, n° 1, janvier 2020, p. 228–259