Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model with a Correlated Random Risk Process

Xiaotao Liu; Hailong Liu

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Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model with a Correlated Random Risk Process

机译：具有相关随机风险过程的方差模型恒定弹性下的保险公司的最佳投资政策

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This paper investigates the optimal portfolio choice problem for a large insurer with negative exponential utility over terminal wealth under the constant elasticity of variance (CEV) model. The surplus process is assumed to follow a diffusion approximation model with the Brownian motion in which is correlated with that driving the price of the risky asset. We first derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation and then obtain explicit solutions to the value function as well as the optimal control by applying a variable change technique and the Feynman–Kac formula. Finally, we discuss the economic implications of the optimal policy.

机译：本文调查了在恒定差异（CEV）模型的恒定弹性下对终端财富的大型保险公司的最佳投资组合选择问题。假设剩余过程遵循与布朗运动的扩散近似模型，其中与驾驶风险资产的价格相关联。我们首先通过应用可变变化技术和Feynman-Kac公式来获得相应的Hamilton-jacobi-bellman（HJB）方程，然后获得对值功能的显式解决方案以及最佳控制。最后，我们讨论了最佳政策的经济影响。

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《Mathematical Problems in Engineering: Theory, Methods and Applications》 |2020年第1期|共10页
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Xiaotao Liu; Hailong Liu;
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1. Optimal investment problem for an insurer with dependent risks under the constant elasticity of variance (CEV) model [J] . YAJIE WANG, XIMIN RONG, HUI ZHAO WSEAS Transactions on Mathematics . 2017,第期

机译：在常量弹性下具有依赖风险的保险公司的最佳投资问题（CEV）模型
2. The Effects of Transaction Cost and Correlation of Brownian Motions on an Insurer’s Optimal Investment Strategy through Logarithmic Utility Optimization under Modified Constant Elasticity of Variance (M-CEV) Model [J] . Silas A. Ihedioha, Gbenga M. Ogungbenle, Philip T. Ajai Open Access Library Journal . 2020,第7期

机译：棕色动作与修改恒定弹性下常量弹性（M-CEV）模型的对数型实用优化对保险公司最优投资策略的影响
3. The optimal investment problem for an insurer and a reinsurer under the constant elasticity of variance model [J] . Li Danping, Rong Ximin, Zhao Hui IMA Journal of Management Mathematics . 2016,第2期

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4. A Semigroup Approach to No-Arbitrage Pricing Theory: Constant Elasticity Variance Model and Term Structure Models [C] . Fabrizio Colombo, Massimiliano Giuli, Vincenzo Vespri International conference on evolution equation . 2003

机译：No-Qualigrage定价理论的半群方法：恒弹性方差模型和术语结构模型
5. The constant elasticity of variance model in the framework of optimal investment problems. [D] . Darius, Dries. 2005

机译：最优投资问题框架下的方差常数弹性模型。
6. Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model [O] . Takashi Shinzato -1

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7. Optimal Investment Problem with Multiple Risky Assets under the Constant Elasticity of Variance (CEV) Model [O] . Hui Zhao, Ximin Rong, Weiqin Ma, 2012

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Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model with a Correlated Random Risk Process

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