[Paper Review] Optimal Dividend Payments under Fixed Cost and Implementation Delays for Various Models

Erhan Bayraktar, Masahiko Egami|arXiv (Cornell University)|Mar 28, 2007

Healthcare Policy and Management5 references2 citations

TL;DR

This paper solves the optimal dividend distribution problem for firms facing regulatory implementation delays, using mean-reverting cash reservoir models (Ornstein-Uhlenbeck and square-root processes). It introduces a novel characterization of the value function for one-dimensional diffusions and provides implementable algorithms to determine optimal controls and value functions under fixed transaction costs and delays.

ABSTRACT

In this paper we solve the dividend optimization problem for a corporation or a financial institution when the managers of the corporation are facing (regulatory) implementation delays. We consider several cash reservoir models for the firm including two mean-reverting processes, Ornstein-Uhlenbeck and square-root processes. We provide our solution via a new characterization of the value function for one-dimensional diffusions and provide easily implementable algorithms to find the optimal control and the value function. 1

Motivation & Objective

• To address the challenge of delayed implementation in dividend distribution decisions for financial institutions and corporations.
• To model the firm's cash reservoir using mean-reverting processes such as Ornstein-Uhlenbeck and square-root processes.
• To incorporate fixed transaction costs and implementation delays into the dividend optimization framework.
• To develop a new characterization of the value function for one-dimensional diffusions applicable to this class of problems.
• To provide computationally feasible algorithms for determining the optimal dividend control and value function.

Proposed method

• Utilizes a novel characterization of the value function tailored for one-dimensional diffusion processes under delay and fixed cost constraints.
• Applies the theory of optimal stopping and impulse control to model dividend payments with implementation delays.
• Employs dynamic programming principles to derive the Hamilton-Jacobi-Bellman (HJB) equation for the value function.
• Derives conditions under which dividend payments are optimal, based on the state of the cash reservoir and delay dynamics.
• Develops numerical algorithms that are easily implementable for computing the optimal control and value function.
• Considers two specific mean-reverting models: the Ornstein-Uhlenbeck and square-root processes, to validate the framework.

Experimental results

Research questions

• RQ1 How do implementation delays affect the optimal dividend policy in a mean-reverting cash reservoir model?
• RQ2 What is the structure of the value function for one-dimensional diffusions under fixed costs and delays?
• RQ3 How can the optimal dividend control be characterized and computed efficiently under these constraints?
• RQ4 What are the implications of using different mean-reverting processes (Ornstein-Uhlenbeck vs. square-root) on optimal dividend strategies?
• RQ5 Can a general framework be developed that unifies the solution of dividend problems with delays and fixed costs across various diffusion models?

Key findings

• The paper establishes a new, general characterization of the value function for one-dimensional diffusions under fixed costs and implementation delays.
• The proposed method enables the derivation of the optimal dividend control policy through easily implementable numerical algorithms.
• The solution framework is applicable to both Ornstein-Uhlenbeck and square-root processes, demonstrating robustness across different mean-reverting dynamics.
• The value function and optimal control are shown to depend critically on the timing and cost structure of dividend payments due to implementation delays.
• The results provide a computationally tractable approach to solving impulse control problems with delays, extending classical dividend optimization models.
• The framework allows for precise determination of the optimal threshold levels for dividend payouts under delayed execution.