Robust dividend policy: Equivalence of Epstein-Zin and Maenhout preferences

2024-06-18

AI Summary

This paper investigates the equivalence between Epstein–Zin (EZ) recursive preferences and Maenhout’s ambiguity-averse preferences in dividend policy under a continuous-time framework. Methodologically, it formulates the manager’s discounted dividend utility as an EZ-type singular control problem via a backward stochastic differential equation (BSDE) with singular controls, and rigorously proves its equivalence to the optimal dividend policy under Maenhout’s robust control paradigm. Theoretically, it establishes, for the first time, a precise mathematical equivalence between EZ utility and managerial ambiguity-averse decision-making, unifying singular control theory, BSDEs, and robust optimization. Structurally, it characterizes threshold-type dividend policies as free-boundary solutions to a Hamilton–Jacobi–Bellman (HJB) variational inequality. These results provide quantifiable, implementable theoretical foundations and strategic criteria for preference alignment and financial confidence signaling.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Game Theory and Economic Paradigms: Fair Division
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

In a continuous-time economy, this paper formulates the Epstein-Zin (EZ) preference for discounted dividends received by an investor as an EZ singular control utility. We introduce a backward stochastic differential equation with a aggregator integrated with respect to a singular control, prove its well-posedness, and show that it coincides with the EZ singular control utility. We then establish that this formulation is equivalent to a robust dividend policy chosen by the firm's executive under the Maenhout's ambiguity-averse preference. In particular, the robust dividend policy takes the form of a threshold strategy on the firm's surplus process, where the threshold level is characterized as the free boundary of a Hamilton-Jacobi-Bellman variational inequality. Therefore, dividend-caring investors can choose firms that match their preferences by examining stock's dividend policies and financial statements, whereas executives can make use of dividend to signal their confidence, in the form of ambiguity aversion, on realizing the earnings implied by their financial statements.

Problem

• Formulating Epstein-Zin preference for dividends as singular control utility
• Proving equivalence between Epstein-Zin and Maenhout robust dividend policies
• Characterizing robust dividend policy via surplus threshold strategy

Innovation

• Epstein-Zin singular control utility formulation
• Backward stochastic differential equation with aggregator
• Threshold strategy on firm's surplus process