CIR模型下保险公司最优投资再保险策略研究  

Optimal Reinsurance and Investment Strategies under CIR Stochastic Interest Rate Model

作　　者：周蕊 荣喜民 赵慧 ZHOU Rui,RONG Ximin,ZHAO Hui(School of Mathematics,Tianjin University,Tianjin 30035)

机构地区：[1]天津大学数学学院,天津300350

出　　处：《工程数学学报》2018年第3期245-257,共13页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11201335;11301376)~~

摘　　要：本文主要研究Cox-Ingersoll-Ross(CIR)随机利率模型下保险公司的最优投资和再保险问题.假设保险公司投资于金融市场中的无风险资产、零息债券和多种股票.此外保险公司购买比例再保险合约以转移承保风险.模型中,我们用仿射过程刻画随机利率,通过扩散过程模拟保险公司盈余过程,即用连续过程近似跳过程.保险公司的目标是通过保险投资最大化终端财富的期望幂效用.由于保险公司的财富过程不是自融资过程,在求解过程中,我们先将原优化问题转化为自融资问题,通过随机最优控制方法导出相应的HJB方程,进而得到最优投资、再保险策略和幂效用函数下的最优值函数.我们发现随着风险厌恶系数的增大,公司投资于股票的比例会降低,初始利率越高,保险公司终端财富的值函数越大.最后,我们给出了保费率、利率参数和风险厌恶系数对投资策略、投资效用的敏感性分析.This paper considers an optimal reinsurance and optimal investment problem under the Cox-Ingersoll-Roll （CIR） stochastic interest rate framework. We assume that the insurer can invest in cash,zero coupon bond and several kinds of stocks in the financial market. Meanwhile,proportion reinsurance is purchased by an insurer to transfer the risk of insurance to other insurance companies. We further adopt an affine CIR model to characterize the interest rate while the surplus wealth process is approximated by a diffusion process, namely, the jump process is approximated by a continuous process. The goal of the insurer is to maximize the expected power utility of the terminal wealth. Due to the fact that the surplus process of the insurer is not a self-financing process, we firstly transform the original problem into a self-financing problem, establish the corresponding Hamilton-Jacobi-Bellman equation, and then derive an explicit solution via the stochastic optimal control method. We find that the percentage of quota invested in stocks would decrease with the increase of risk aversion parameters, while the terminal wealth would increase with the increase of initial interest rate. Finally, sensitivity analysis is carried out to show the impact of financial parameters on the optimal strategies and optimal utility.

关 键 词：CIR随机利率模型 投资策略 再保险 幂效用 随机最优控制 

分 类 号：F224.3[经济管理—国民经济]