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

Kexin Chen, Kyunghyun Park, Hoi Ying Wong

TL;DR

The paper develops a unified framework linking Epstein–Zin recursive utilities for singular dividend flows with Maenhout's robust ambiguity-averse preference in a continuous-time setting with bankruptcy risk. It proves the well-posedness of the EZ singular-control utility via BSDEs with random terminal time, and shows that the EZ value equals the Maenhout robust value raised to the power $1-\mathcal{R}$, establishing a precise equivalence between the two preferences under ambiguity. It further characterizes the robust optimal policy as a threshold strategy determined by a free boundary in a HJB-VI, and provides a comprehensive shooting method to prove existence and uniqueness of the optimal threshold. Sensitivity analysis reveals how ambiguity aversion shapes the robust value and the threshold, including a smooth convergence to the ambiguity-neutral benchmark as $\mathcal{R}\to0$. Collectively, the results offer a tractable, market-signaling interpretation: executives can signal earnings confidence through robust dividends, while investors can select firms whose dividend policies align with their EZ or robust preferences.

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.

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

TL;DR

The paper develops a unified framework linking Epstein–Zin recursive utilities for singular dividend flows with Maenhout's robust ambiguity-averse preference in a continuous-time setting with bankruptcy risk. It proves the well-posedness of the EZ singular-control utility via BSDEs with random terminal time, and shows that the EZ value equals the Maenhout robust value raised to the power , establishing a precise equivalence between the two preferences under ambiguity. It further characterizes the robust optimal policy as a threshold strategy determined by a free boundary in a HJB-VI, and provides a comprehensive shooting method to prove existence and uniqueness of the optimal threshold. Sensitivity analysis reveals how ambiguity aversion shapes the robust value and the threshold, including a smooth convergence to the ambiguity-neutral benchmark as . Collectively, the results offer a tractable, market-signaling interpretation: executives can signal earnings confidence through robust dividends, while investors can select firms whose dividend policies align with their EZ or robust preferences.

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.
Paper Structure (12 sections, 26 theorems, 197 equations)

This paper contains 12 sections, 26 theorems, 197 equations.

Table of Contents

  1. Introduction
  2. Stochastic differential utility on singular dividend flows
  3. Robust formulation of singular dividend flows
  4. Characterization of robust singular dividend flow
  5. Sensitivity analysis with respect to ambiguity aversion
  6. Proof of Theorem \ref{['thm:recurs_BSDE']} ii.
  7. Proof of Proposition \ref{['prop:v_bound_con']}
  8. Proof of Theorem \ref{['thm:shooting']}
  9. Preliminary lemmas for Proposition \ref{['pro:shooting_sub']}
  10. Proof of Proposition \ref{['pro:shooting_sub']}.
  11. Proof of Theorem \ref{['thm:verification']}
  12. Proofs of results in Section \ref{['sec:5']}

Key Result

Theorem 2.5

Let $(\tau, D, \xi_{\tau})$ satisfy Condition cond:triplet, and let $g_{\mathrm{EZ}}(\cdot, \cdot)$ be defined as in dfn:g_EZ. Then the following statements hold:

Theorems & Definitions (64)

  • Definition 2.1
  • Definition 2.2
  • Remark 2.3
  • Definition 2.4
  • Theorem 2.5
  • proof : Proof of Theorem \ref{['thm:recurs_BSDE']} i.
  • Remark 2.6
  • Definition 3.1
  • Proposition 3.2
  • proof
  • ...and 54 more