Equilibrium singular dividend control under ambiguity aggregation of heterogeneous discount rates

2026-06-24

AI Summary

This study addresses the singular dividend control problem for firms with heterogeneous shareholders under ambiguity aggregation, tackling the resulting time inconsistency. By introducing an ambiguity aggregation function to capture shareholder heterogeneity and ambiguity attitudes, the authors construct a time-homogeneous equilibrium strategy that partitions the state space into a waiting region and a dividend-payout region, and establish a corresponding verification theorem. For the first time within a singular control framework, they jointly incorporate the distribution of discount rates and ambiguity aggregation, proving the existence of a unique barrier-type equilibrium under linear and exponential aggregation functions—even with unbounded dividend rates—while showing that such equilibria do not exist under power or logarithmic aggregation functions. Numerical experiments further demonstrate the significant impact of discount rate heterogeneity and ambiguity aversion on the equilibrium barrier.

Abstract

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.

Problem

• singular dividend control
• heterogeneous discount rates
• ambiguity aggregation
• time inconsistency
• equilibrium strategy

Innovation

• singular dividend control
• ambiguity aggregation
• heterogeneous discount rates
• time-inconsistent equilibrium
• barrier-type equilibrium