Paper: arXiv 2406.12305

Authors: Kexin Chen, Kyunghyun Park, Hoi Ying Wong

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.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous theoretical contribution establishing mathematical equivalence between Epstein-Zin recursive utility and Maenhout ambiguity aversion in a singular stochastic control framework with BSDEs. However, it is purely theoretical with no empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Model Robust Dividend Policy & Link<br>Epstein-Zin to Maenhout Preferences"] --> B["Methodology:<br>Formulate Epstein-Zin Utility as a<br>Singular Control Problem"]
    B --> C["Mathematical Framework:<br>Develop & Prove Well-Posedness of BSDE<br>with Singular Control Aggregator"]
    C --> D["Optimization & Equivalence:<br>Solve HJB Variational Inequality for<br>Ambiguity-Averse (Maenhout) Executive"]
    D --> E["Core Outcome:<br>Prove Preference Equivalence & Derive<br>Threshold Strategy (Free Boundary)"]
    E --> F["Practical Application:<br>Investors match preferences via dividends;<br>Executives signal earnings confidence"]

Cited References (145)

  1. Optimal risk exposure and dividend payout policies under model uncertainty (2021)
  2. Model Ambiguity versus Model Misspecification in Dynamic Portfolio Choice (2025)
  3. INITIAL INVESTMENT CHOICE AND OPTIMAL FUTURE ALLOCATIONS UNDER TIME-MONOTONE PERFORMANCE CRITERIA (2011)
  4. An Exact Connection between Two Solvable SDEs and a Nonlinear Utility Stochastic PDE (2013)
  5. Portfolio choice under dynamic investment performance criteria (2009)
  6. Portfolio Choice under Space-Time Monotone Performance Criteria (2010)
  7. Representation of Homothetic Forward Performance Processes in Stochastic Factor Models via Ergodic and Infinite Horizon BSDE (2017)
  8. Stochastic Integration and Differential Equations (2003)
and 137 more
  1. Fundamentals of Differential Equations And Boundary Value Problems (2017)
  2. OPTIMAL DIVIDEND POLICY WITH MEAN-REVERTING CASH RESERVOIR (2007)
  3. Continuous martingales and Brownian motion (1999)
  4. On boundary crossing probabilities for diffusion processes (2010)
  5. Decomposition of Optimal Portfolio Weight in a Jump-Diffusion Model and Its Applications (2012)
  6. A new proof for comparison theorems for stochastic differential inequalities with respect to semimartingales (1998)
  7. A class of stochastic Gronwall’s inequality and its application (2018)
  8. Adapted solution of a backward stochastic differential equation (1990)
  9. Backward stochastic differential equations with random stopping time and singular final condition (2007)
  10. $L^p$ solutions of backward stochastic differential equations (2003)
  11. Controlled Markov processes and viscosity solutions (2006)
  12. Stochastic Differential Utility (1992)
  13. Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework (1989)
  14. PDE solutions of stochastic differential utility (1992)
  15. Optimal Consumption and Portfolio Selection with Stochastic Differential Utility (1999)
  16. Risk-sensitive dividend problems (2015)
  17. Backward stochastic differential equations with rough drivers (2012)
  18. Singular recursive utility (2017)
  19. Backward Stochastic Differential Equations in Finance (1997)
  20. Preferences for partial information and ambiguity (2020)
  21. A Generalized Stochastic Differential Utility (2003)
  22. Backward stochastic differential equations in finance (1997)
  23. One-dimensional BSDE s with finite and infinite time horizons (2011)
  24. Infinite time interval BSDE s and the convergence of g-martingales (2000)
  25. Differentiating ambiguity and ambiguity attitude (2004)
  26. Ambiguity, risk, and asset returns in continuous time (2002)
  27. Intertemporal asset pricing under Knightian uncertainty (2004)
  28. Backward stochastic differential equations with constraints on the gains-process (1998)
  29. On a class of path-dependent singular stochastic control problems (2018)
  30. Temporal Resolution of Uncertainty and Dynamic Choice Theory (1978)
  31. Recursive Utility and Preferences for Information (1998)
  32. Point processes and queues: martingale dynamics (1981)
  33. Robo-Advising: Learning Investors’ Risk Preferences via Portfolio Choices* (2020)
  34. Consumption–investment optimization with Epstein–Zin utility in incomplete markets (2017)
  35. Singular Stochastic Control, Linear Diffusions, and Optimal Stopping: A Class of Solvable Problems (2001)
  36. A class of singular stochastic control problems (1983)
  37. Optimal Harvesting from Interacting Populations in a Stochastic Environment (2001)
  38. Optimal harvesting, economic discounting and extinction risk in fluctuating populations (1994)
  39. Irreversible investment and industry equilibrium (1996)
  40. Firm behaviour under the threat of liquidation (1996)
  41. Strategies for Dividend Distribution: A Review (2009)
  42. Robust control and recursive utility (2003)
  43. Risk, uncertainty and profit (1921)
  44. Robust control and model uncertainty (2001)
  45. G-Brownian motion and dynamic risk measure under volatility uncertainty (2007) — link
  46. Optimal reduction of public debt under partial observation of the economic growth (2020)
  47. Optimal dividends with partial information and stopping of a degenerate reflecting diffusion (2020)
  48. Two-sided singular control of an inventory with unknown demand trend (2021)
  49. Nonlinear filtering of partially observed systems arising in singular stochastic optimal control (2022)
  50. Singular stochastic control and optimal stopping with partial information of It^ o –L' e vy processes (2012)
  51. Testing negative value of information and ambiguity aversion (2023)
  52. Partial Ambiguity (2017)
  53. Learning agents for uncertain environments (1998)
  54. Algorithms for inverse reinforcement learning. (2000)
  55. Inverse optimization (2001)
  56. Learning risk preferences from investment portfolios using inverse optimization (2023)
  57. The promises and pitfalls of robo-advising (2019)
  58. Proper solutions for Epstein–Zin stochastic differential utility (2025)
  59. Multidimensional singular control and related Skorokhod problem: Sufficient conditions for the characterization of optimal controls (2023)
  60. On singular control for L 'e vy processes (2023)
  61. Generalized inverse optimization through online learning (2018)
  62. Irreversible Consumption Habit under Ambiguity: Singular Control and Optimal $G$ -Stopping Time (2025)
  63. Duality in optimal consumption–investment problems with alternative data (forthcoming)
  64. Optimal retirement under partial information (2022)
  65. Fundamentals of stochastic filtering (2009)
  66. Revisiting the dividend puzzle: Do all of the pieces now fit? (2002)
  67. Epstein-Zin utility maximization on a random horizon (2023)
  68. Optimal dividend problem with a terminal value for spectrally positive L 'e vy processes (2013)
  69. Epstein-Zin utility maximization on a random horizon (2023)
  70. Diffusions, Markov Processes and Martingales (2000)
  71. A diffusion model for optimal dividend distribution for a company with constraints on risk control (2003)
  72. The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. II: Existence, uniqueness and verification for $\vartheta\in(0, 1)$ (2023)
  73. Backward stochastic differential equations with rough drivers
  74. The infinite-horizon investment–consumption problem for Epstein–Zin stochastic differential utility. I: Foundations (2023)
  75. Limit Theorems for Stochastic Processes (2013)
  76. Backward stochastic differential equations and partial differential equations with quadratic growth (2000)
  77. An Explicit Formula for the Skorokhod Map on $[0, a]$ (2007)
  78. Optimal dividends under model uncertainty (2023)
  79. Optimal ergodic harvesting under ambiguity (2022)
  80. A class of solvable stochastic dividend optimization problems: on the general impact of flexibility on valuation (2006)
  81. On the martingale property of certain local martingales (2012)
  82. Handbook of Brownian Motion – Facts And Formulae (2015)
  83. Robust control and model misspecification (2006)
  84. Robust portfolio rules and asset pricing (2004)
  85. A pseudo-Markov property for controlled diffusion processes (2016)
  86. Brownian Motion and Stochastic Calculus (1991)
  87. Robust control and model misspecification. (2006)
  88. The dividend puzzle. (1976)
  89. Dividend policy, growth, and the valuation of shares. (1961)
  90. Imperfect information, dividend policy, and ``the bird in the hand’’ fallacy. (1979)
  91. Dividends, dilution, and taxes: A signalling equilibrium. (1985)
  92. Dividend Policy under Asymmetric Information. (1985)
  93. Noise. (1986)
  94. Payout policy in the 21st century. (2005)
  95. Do dividends convey information about future earnings? (2020)
  96. Disappearing and reappearing dividends. (2022)
  97. Signaling safety. (2021)
  98. Optimal dividend policies with random profitability. (2020)
  99. Stochastic differential utility. (1992)
  100. Optimization of the flow of dividends (1995)
  101. Optimal consumption for general diffusions with absorbing and reflecting barriers (1984)
  102. Optimal consumption and investment with Epstein–Zin recursive utility (2017)
  103. Convex duality for Epstein–Zin stochastic differential utility (2018)
  104. Lifetime investment and consumption with recursive preferences and small transaction costs (2020)
  105. A free boundary problem related to singular stochastic control: the parabolic case (1991)
  106. On an integral equation for the free-boundary of stochastic, irreversible investment problems (2015)
  107. Optimal boundary surface for irreversible investment with stochastic costs (2017)
  108. A free boundary problem related to singular stochastic control (1991)
  109. Optimal control under a dynamic fuel constraint (2005)
  110. A stochastic representation theorem with applications to optimization and obstacle problems (2004)
  111. CONVEX DUALITY FOR STOCHASTIC SINGULAR CONTROL PROBLEMS (2017)
  112. Optimal consumption choice with intertemporal substitution (2001)
  113. Optimal consumption with Hindy–Huang–Kreps preferences under nonlinear expectations (2022)
  114. A Knightian irreversible investment problem (2022)
  115. On the multidimensional controller-and-stopper games (2013)
  116. Optimal stopping for non-linear expectations— Part I (2011)
  117. Optimal stopping for non-linear expectations— Part II (2011)
  118. Robust retirement and life insurance with inflation risk and model ambiguity (2023)
  119. Robust Retirement with Return Ambiguity: Optimal $G$ -Stopping Time in Dual Space (2023)
  120. Robust portfolio rules and detection-error probabilities for a mean-reverting risk premium (2006)
  121. Dynamic asset allocation with uncertain jump risks: a pathwise optimization approach (2018)
  122. A quartet of semigroups for model specification, robustness, prices of risk, and model detection (2003)
  123. Robust portfolio choice and indifference valuation (2014)
  124. $I$ -divergence geometry of probability distributions and minimization problems (1975)
  125. The entropic penalty approach to stochastic programming (1985)
  126. Robust portfolio choice with uncertainty about jump and diffusion risk (2013)
  127. Robust optimal control for an insurer with reinsurance and investment under Heston’s stochastic volatility model (2013)
  128. OPTIMAL STOPPING UNDER ADVERSE NONLINEAR EXPECTATION AND RELATED GAMES (2015)
  129. Optimal stopping with multiple priors (2009)
  130. Optimal excess-of-loss reinsurance contract with ambiguity aversion in the principal-agent model (2020)
  131. Stability of the Epstein–Zin problem (2024)
  132. Sensitivity of robust optimization problems under drift and volatility uncertainty — → 2311.11248
  133. Model uncertainty, recalibration, and the emergence of delta–vega hedging (2017)
  134. Hedging with small uncertainty aversion (2017)
  135. Numerical method for nonlinear Kolmogorov PDEs via sensitivity analysis (2026)
  136. Continuous martingales and Brownian motion (2013)
  137. Sensitivity Analysis of Distributionally Robust BSDEs and RBSDEs (2025) — link

1 of 145 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.