Paper: arXiv 2508.12047
Authors: Jingyi Cao, Dongchen Li, Virginia R. Young, Bin Zou
Abstract
This paper studies an optimal dividend problem for a company that aims to maximize the mean-variance (MV) objective of the accumulated discounted dividend payments up to its ruin time. The MV objective involves an integral form over a random horizon that depends endogenously on the company’s dividend strategy, and these features lead to a novel time-inconsistent control problem. To address the time inconsistency, we seek a time-consistent equilibrium dividend rate strategy. We first develop and prove a new verification lemma that characterizes the value function and equilibrium strategy by an extended Hamilton-Jacobi-Bellman system. Next, we apply the verification lemma to obtain the equilibrium strategy and show that it is a barrier strategy for small levels of risk aversion.
Complexity vs Empirical Score
- Math Complexity: 8.5/10
- Empirical Rigor: 1.5/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper provides a rigorous mathematical theoretical framework for a novel time-inconsistent stochastic control problem in optimal dividend theory using mean-variance optimization. However, it is purely theoretical and lacks empirical backtesting or real-world data validation.
Research Flowchart
flowchart TD
A[Research Goal: Optimal Dividend Strategy under Mean-Variance Objective & Ruin Risk] --> B[Model Formulation: Random Horizon Time-Inconsistent Control]
B --> C[Inputs: Dividend Rate, Discount Factor, Ruin Time, Risk Aversion Parameter]
C --> D[Methodology: Develop New Verification Lemma via Extended HJB System]
D --> E[Computation: Solve Extended HJB System for Value Function & Equilibrium Strategy]
E --> F[Findings: Characterized Time-Consistent Equilibrium Strategy]
F --> G[Outcome: Strategy Proven to be Barrier Strategy for Small Risk Aversion]