Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate

TL;DR

This paper explores two methods for maximizing dividends in a setting with stochastic Ornstein-Uhlenbeck interest rates, including negative rates, using analytical and stochastic differential equation techniques.

Contribution

It introduces two novel approaches for dividend maximization under Ornstein-Uhlenbeck interest rates, providing explicit strategies and analyzing their properties.

Findings

Explicit separating curve for optimal strategy at deterministic times

Analysis of properties of optimal control problems using HJB equations

Behavior of strategies with negative interest rates

Abstract

We investigate a dividend maximization problem under stochastic interest rates with Ornstein-Uhlenbeck dynamics. This setup also takes negative rates into account. First a deterministic time is considered, where an explicit separating curve $\alpha(t)$ can be found to determine the optimal strategy at time $t$. In a second setting we introduce a strategy-independent stopping time. The properties and behavior of these optimal control problems in both settings are analyzed in an analytical HJB-driven approach as well as using backward stochastic differential equations.