  Adopting a probabilistic approach we determine the optimal dividend payout
policy of a firm whose surplus process follows a controlled arithmetic Brownian
motion and whose cash-flows are discounted at a stochastic dynamic rate.
Dividends can be paid to shareholders at unrestricted rates so that the problem
is cast as one of singular stochastic control. The stochastic interest rate is
modelled by a Cox-Ingersoll-Ross (CIR) process and the firm's objective is to
maximize the total expected flow of discounted dividends until a possible
insolvency time. We find an optimal dividend payout policy which is such that
the surplus process is kept below an endogenously determined stochastic
threshold expressed as a decreasing continuous function $r \mapsto b(r)$ of the
current interest rate value. We also prove that the value function of the
singular control problem solves a variational inequality associated to a
second-order, non-degenerate elliptic operator, with a gradient constraint.
