  In this paper, we consider the problem of maximizing the expected discounted
utility of dividend payments for an insurance company that controls risk
exposure by purchasing proportional reinsurance. We assume the preference of
the insurer is of CRRA form. By solving the corresponding
Hamilton-Jacobi-Bellman equation, we identify the value function and the
corresponding optimal strategy. We also analyze the asymptotic behavior of the
value function for large initial reserves. Finally, we provide some numerical
examples to illustrate the results and analyze the sensitivity of the
parameters.
