Paper: arXiv 2502.05839

Authors: Wenyuan Wang, Zuo Quan Xu, Kazutoshi Yamazaki, Kaixin Yan, Xiaowen Zhou

Abstract

In this paper, we examine a modified version of de Finetti’s optimal dividend problem, incorporating fixed transaction costs and altering the surplus process by introducing two-valued drift and two-valued volatility coefficients. This modification aims to capture the transitions or adjustments in the company’s financial status. We identify the optimal dividend strategy, which maximizes the expected total net dividend payments (after accounting for transaction costs) until ruin, as a two-barrier impulsive dividend strategy. Notably, the optimal strategy can be explicitly determined for almost all scenarios involving different drifts and volatility coefficients. Our primary focus is on exploring how changes in drift and volatility coefficients influence the optimal dividend strategy.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly rigorous mathematical analysis of de Finetti’s optimal dividend problem under endogenous regime switching with fixed transaction costs. While it demonstrates strong mathematical depth and analytical novelty in solving the associated QVI, it is entirely theoretical and completely lacks empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve de Finetti's dividend problem with fixed costs & regime switching] --> B[Input: Surplus Process with two-valued drift/volatility & fixed transaction costs]
    B --> C[Methodology: Formulate Stochastic Control Problem & Hamilton-Jacobi-Bellman Equations]
    C --> D[Computational Process: Derivation of Value Functions & Verification Theorems]
    D --> E[Outcome: Optimal dividend strategy is a Two-Barrier Impulsive Strategy]
    E --> F[Findings: Explicit solutions determined & sensitivity to drift/volatility analyzed]