This paper studies an optimal excess-of-loss reinsurance and investment problem in a model with delay and jumps for an insurer, who can purchase excess-of-loss reinsurance and invest his surplus in a risk-free asset and a risky asset whose price is governed by a jump-diffusion model. The insurer’s surplus is described by a diffusion model, which is an approximation of the classical compound Poisson risk model. In particular, the wealth process of the insurer is modeled by a stochastic differential delay equation via introducing the performance-related capital inflow or outflow. Under the criterion for maximizing the expected exponential utility of the combination of terminal wealth and average performance wealth, optimal strategy and the corresponding value function are obtained by using the dynamic programming approach. Finally, numerical examples are provided to show the effects of model parameters on the optimal strategies and illustrate the economic meaning.

中文翻译：

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时滞和跳跃模型下保险公司的最优再保险和投资策略

本文研究了一个具有时滞和跳跃的模型的最优损失超额再保险和投资问题，该保险公司可以购买损失超额再保险并将其盈余投资于无风险资产和其价格具有风险的资产由跳跃扩散模型控制。保险公司的盈余由扩散模型描述，该模型是经典复合Poisson风险模型的近似值。特别地，通过引入与绩效相关的资本流入或流出，通过随机的微分延迟方程对保险公司的财富过程进行建模。在最大化终端财富和平均绩效财富的组合的期望指数效用的准则下，采用动态规划方法获得了最优策略和相应的价值函数。最后，