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Optimal dividend payout with path-dependent drawdown constraint

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Listed:
  • Chonghu Guan
  • Jiacheng Fan
  • Zuo Quan Xu

Abstract

This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic control problem, as the admissible control depends on its own past values. The associated Hamilton-Jacobi-Bellman (HJB) equation is a novel two-dimensional variational inequality with a gradient constraint, a type of problem previously only analyzed in the literature using viscosity solution techniques. In contrast, this paper employs delicate PDE methods to establish the existence of a strong solution. This stronger regularity allows us to explicitly characterize an optimal feedback control strategy, expressed in terms of two free boundaries and the running maximum surplus process. Furthermore, we derive key properties of the value function and the free boundaries, including boundedness and continuity. Numerical examples are provided to verify the theoretical results and to offer new financial insights.

Suggested Citation

  • Chonghu Guan & Jiacheng Fan & Zuo Quan Xu, 2023. "Optimal dividend payout with path-dependent drawdown constraint," Papers 2312.01668, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2312.01668
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    References listed on IDEAS

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    Cited by:

    1. Mingxin Guo & Zuo Quan Xu, 2024. "Stochastic optimal self-path-dependent control: A new type of variational inequality and its viscosity solution," Papers 2412.11383, arXiv.org.

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