| In this paper, we consider an insurance company which can invest its asset in n risky stocks, one riskless bond as well as purchasing proportional reinsurance. In order to control the investment risk when pursuing the maximized exponential utility of terminal wealth. Classical value-at-risk constraints and its variations(Conditional-VaR, Proportional-VaR) are imported on the total wealth. By numerically solving the corresponding Hamilton-Jacobi-Bellman equation, we derive the optimal investment strategies. Furthermore, the impact on constrained optimal strategy made by the changes of safety loadings has been investigated. Optimal investment strategies derived from different VaR constraints are compared with each other, which indicates the essential difference among these risk measures. |
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