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Yue Cao, Guohui Guan, Zongxia Liang, Xiaodong Luo · 2026-06-24
The paper builds a mathematical model of how a firm should pay dividends when its shareholders disagree about how much they discount future payoffs. Because aggregating these differing preferences creates 'time-inconsistent' incentives, the authors look for a stable ('equilibrium') dividend rule defined by thresholds separating when to hold cash versus pay out, and prove when such barrier-type rules exist or don't (they exist under linear and exponential aggregation, but not under power-type or logarithmic).
Why it matters: It offers a theoretical lens on how shareholder heterogeneity and ambiguity aversion might shift a firm's optimal dividend-payout threshold. A practitioner interested in corporate payout policy or firm valuation might find the intuition useful, though the work is abstract and mathematical rather than a directly usable tool.
⚠ This is a theoretical optimal-control result with stylized assumptions and numerical illustrations, not an empirically tested or directly tradable strategy.
This paper studies a singular dividend control problem for a firm with heterogeneous shareholders whose discount rates follow a given distribution. The central planner aggregates expected discounted payoffs using an ambiguity aggregation function $phi$, which captures shareholder heterogeneity and ambiguity attitudes but also leads to time inconsistency. To address this issue, we seek a time-homogeneous equilibrium dividend law characterized by a partition of the state space into waiting and dividend-paying regions. We provide a rigorous mathematical characterization by proving a verification theorem and deriving necessary conditions for the equilibrium law. We then analyze barrier-type equilibria, showing non-existence for a class of aggregation functions that includes power-type and logarithmic aggregation functions, and establishing existence and uniqueness under linear and exponential aggregation. In the linear case, the bounded-rate equilibrium is shown to converge to the singular barrier-type equilibrium as the dividend rate bound tends to infinity. Numerical examples illustrate the effects of discount-rate heterogeneity and ambiguity aversion on the equilibrium barrier.
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AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.