  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.
