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

TL;DR

This paper demonstrates the equivalence between Epstein-Zin and Maenhout preferences in a continuous-time setting, linking robust dividend policies with ambiguity aversion and threshold strategies.

Contribution

It introduces a novel formulation of Epstein-Zin preferences as a singular control utility and proves its equivalence to robust dividend policies under ambiguity aversion.

Findings

The Epstein-Zin singular control utility is well-posed and coincides with a backward stochastic differential equation.

Robust dividend policies are characterized as threshold strategies based on a free boundary problem.

Dividend policies can serve as signals of firm confidence and ambiguity aversion.

Abstract

In a continuous-time economy, this paper formulates the Epstein-Zin preference for discounted dividends received by an investor as an Epstein-Zin singular control utility. We introduce a backward stochastic differential equation with an aggregator integrated with respect to a singular control, prove its well-posedness, and show that it coincides with the Epstein-Zin 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.