Optimal dividend policies with random profitability

Max Reppen, Jean Rochet and Mete Soner
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Max Reppen: ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]
Mete Soner: ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich]

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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 Ornsteinâ€"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 Hamiltonâ€"Jacobiâ€"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 (search for similar items in EconPapers)
Date: 2020-01
Note: View the original document on HAL open archive server: https://hal.science/hal-02929766v1
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Citations: View citations in EconPapers (11)

Published in Mathematical Finance, 2020, 30 (1), pp.228-259. ⟨10.1111/mafi.12223⟩

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Related works:
Journal Article: Optimal dividend policies with random profitability (2020)
Working Paper: Optimal dividend policies with random profitability (2018)
Working Paper: Optimal dividend policies with random profitability (2018)
Working Paper: Optimal dividend policies with random profitability (2018)
Working Paper: Optimal Dividend Policies with Random Profitability (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02929766

DOI: 10.1111/mafi.12223

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