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Assume that an insurer has two dependent lines of business. The reserves of the two lines of business are modeled by a two-dimensional compound Poisson risk process or a common shock model. To protect from large losses and to reduce the ruin probability of the insurer, the insurer applies a reinsurance policy to each line of business, thus the two policies form a two-dimensional reinsurance policy. In this paper, we investigate the two-dimensional reinsurance policy in a dynamic setting. By using the martingale central limit theorem, we first derive a two-dimensional diffusion approximation to the two-dimensional compound Poisson reserve risk process. We then formulate the total reserve of the insurer by a controlled diffusion process and reduce the problem of optimal reinsurance strategies to a dynamic control problem for the controlled diffusion process. Under this setting, we show that a two-dimensional …