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Optimal excess-of-loss reinsurance and investment problem with delay and jump-diffusion risk process under the CEV model

机译:CEV模型下的延迟和跳跃扩散风险过程的最佳过度损失再保险和投资问题

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In this paper, we investigate an optimal investment and excess-of-loss reinsurance problem with delay and jump-diffusion risk process for an insurer. Specifically, the insurer is allowed to purchase excess-of-loss reinsurance and invest in a financial market, where the surplus of insurer is represented by a jump-diffusion model and the financial market consists of one risk-free asset and one risky asset whose price process is governed by a constant elasticity of variance model. In addition, the performance-related capital inflow/outflow is introduced, the wealth process of insurer is modeled by a stochastic differential delay equation. The insurer aims to seek the optimal excess-of-loss reinsurance and investment strategy to maximize the expected exponential utility of the combination of terminal wealth and average performance wealth. By solving a Hamilton-jacobi-Bellman equation, the closed-form expressions for the optimal strategy and the optimal value function are derived. Finally, some special cases of our model and results are presented, and some numerical examples for our results are provided. (C) 2018 Elsevier B.V. All rights reserved.
机译:在本文中,我们调查了对保险公司的延迟和跳跃扩散风险过程的最佳投资和过度损失再保险问题。具体而言,保险公司被允许购买过度损失再保险和投资金融市场,保险公司的盈余由跳跃扩散模型代表,金融市场由一个无风险资产和一个风险资产组成价格过程受方差模型的恒定弹性。此外,介绍了性能相关的资本流入/外流,保险公司的财富过程由随机差动延迟方程式进行建模。保险公司旨在寻求最佳的过度损失再保险和投资策略,以最大限度地提高终端财富和平均绩效财富的预期指数效用。通过求解汉密尔顿 - jacobi-bellman方程,得出了最佳策略和最佳价值函数的闭合形式表达式。最后,提供了我们模型和结果的一些特殊情况,提供了一些数字示例。 (c)2018年elestvier b.v.保留所有权利。

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