  We study an optimal dividend problem for an insurer who simultaneously
controls investment weights in a financial market, liability ratio in the
insurance business, and dividend payout rate. The insurer seeks an optimal
strategy to maximize her expected utility of dividend payments over an infinite
horizon. By applying a perturbation approach, we obtain the optimal strategy
and the value function in closed form for log and power utility. We conduct an
economic analysis to investigate the impact of various model parameters and
risk aversion on the insurer's optimal strategy.
