This paper studies the optimal investment and reinsurance problem for a risk model with premium control. It is assumed that the insurance safety loading and the time-varying claim arrival rate are connected through a monotone decreasing function, and that the insurance and reinsurance safety loadings have a linear relationship. Applying stochastic control theory, we are able to derive the optimal strategy that maximizes the expected exponential utility of terminal wealth. We also provide a few numerical examples to illustrate the impact of the model parameters on the optimal strategy.

中文翻译：

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通过保费控制实现最佳投资和再保险

本文研究了具有保费控制的风险模型的最优投资和再保险问题。假设保险安全负荷和时变索赔到达率是通过单调递减函数连接的，并且保险和再保险安全负荷具有线性关系。应用随机控制理论，我们能够得出使终端财富的预期指数效用最大化的最优策略。我们还提供了一些数值示例来说明模型参数对最佳策略的影响。