Paper: arXiv 2610.34348

Authors: Alexandre Roch, Simone Scotti

Abstract

We study an optimal dividend policy problem under ratcheting and bankruptcy constraints. Firms face a tradeoff between the negative signal of a dividend reduction and a potential future bankruptcy. In contrast to previous works, the dividend rate is allowed to decrease after incurring a negative impact on equity valuation in accordance with a large empirical literature on the topic. We provide an explicit necessary and sufficient condition for the finiteness of the value function and prove the differentiability of the value function, and its characterization via viscosity solutions and the so-called supercontact property. The value function is given by the solution of a two-dimensional variational inequality combining optimal stopping, singular and impulse controls. We show that the problem is equivalent to a one-dimensional setup simplifying both mathematical and financial analysis. Finally, we provide a numerical study of the model and a sensitivity analysis with respect to the model parameters. We show the relevance of over-reaction to financial news on the manager’s optimal policy.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly complex mathematical framework for optimal dividend policies, introducing novel elements like dividend resets with equity valuation impacts. While it includes a numerical study and sensitivity analysis, the empirical rigor is limited to theoretical simulations rather than real-world data validation or backtesting. The overall contribution is strong due to its innovative theoretical approach.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Ratcheting Dividend Policy with Resets] --> B{Key Methodology: Variational Inequality & Viscosity Solutions};
    B --> C[Data/Inputs: Equity Valuation, Dividend Rates, Bankruptcy Constraints];
    C --> D{Computational Process: Two-dimensional Variational Inequality Solved by Equivalent One-dimensional Setup};
    D --> E[Key Finding 1: Explicit Necessary & Sufficient Condition for Value Function Finiteness];
    D --> F[Key Finding 2: Differentiability of Value Function, Characterized by Supercontact Property];
    D --> G[Key Finding 3: Relevance of Over-reaction to Financial News on Manager's Policy];
    E & F & G --> H[Outcome: Numerical Study & Sensitivity Analysis of Optimal Policy];