  In this paper we assume the insurance wealth process is driven by the
compound Poisson process. The discounting factor is modelled as a geometric
Brownian motion at first and then as an exponential function of an integrated
Ornstein-Uhlenbeck process. The objective is to maximize the cumulated value of
expected discounted dividends up to the time of ruin. We give an explicit
expression of the value function and the optimal strategy in the case of
interest rate following a geometric Brownian motion. For the case of the
Vasicek model, we explore some properties of the value function. Since we can
not find an explicit expression for the value function in the second case, we
prove that the value function is the viscosity solution of the corresponding
HJB equation.
