Abstract
<p style='text-indent:20px;'>In this paper, we study the optimal investment problem for an insurer, who is allowed to invest in a financial market which consists of <inline-formula><tex-math id="M1">\begin{document}$ N $\end{document}</tex-math></inline-formula> risky securities modeled by an <inline-formula><tex-math id="M2">\begin{document}$ N $\end{document}</tex-math></inline-formula>-dimensional Itô process. The surplus of the insurer is modeled by a general risk model. For the insurer's wealth, some money (called liquid reserves) can only be used to cope with risk, and can not be invested in the financial market. We suggest that the liquid reserve is a proportion of the total claim amount. By the martingale approach, we derive the optimal strategies for the CARA and the quadratic utilities, respectively.
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