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

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.