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We consider an insurer who faces an external jump-diffusion risk that is negatively correlated with the capital returns in a multidimensional regime switching model. The insurer selects investment and liability ratio policies continuously to maximize her/his expected utility of terminal wealth. We obtain explicit solutions of optimal policies for logarithmic and power utility functions. We study the impact of the insurer’s risk aversion, the negative correlation between the external risk and the capital returns, and the regime of the economy on the optimal policy. We find, among other things, that the regime of the economy and the negative correlation between the external risk and the capital returns have a dramatic effect on the optimal policy

Optimal Investment and Liability Ratio Policies in a Multidimensional Regime Switching Model