This paper considers the optimal investment-reinsurance problem with delay for an insurer under a constant elasticity of variance (CEV) model. Suppose that the insurer is allowed to purchase proportion reinsurance and invest her surplus in a financial market consisting of one risk-free asset and one risky asset whose price process is described by a CEV model. Under the consideration of the performance-related capital inflow/outflow, the wealth process of the insurer is modeled by a stochastic delay differential equation (SDDE). The objective of the insurer is to maximize the expected exponential utility of terminal wealth. The optimal strategies and the optimal value functions in the closed form are derived under two cases:the investment-reinsurance case and the investment-only case. Finally, some numerical examples and sensitivity analysis are provided for our results.
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