S型效用下比例再保险的最优投资策略  

Optimal proportional reinsurance and investment problem for insurers with loss aversion

作　　者：孙庆雅 荣喜民 赵慧 SUN Qingya;RONG Ximin;ZHAO Hui(School of Mathematics,Tianjin University,Tianjin 300354,China)

机构地区：[1]天津大学数学学院,天津300354

出　　处：《系统工程理论与实践》2020年第2期284-297,共14页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(11871052,71102118)。

摘　　要：本文引入了行为金融学中的损失厌恶概念,研究考虑损失厌恶时保险公司的最优投资再保险问题.在损失厌恶下,保险公司面对盈利时是风险厌恶者,而遭受损失时转为风险追求者,因此本文采用S型效用函数,并以终端财富的效用最大化为目标求解保险公司的最优策略.假定保险公司的盈余过程服从经典的Cramer-Lundberg模型,可将资产投资于一种无风险资产和一种服从几何布朗运动的风险资产,且可以通过向再保险公司购买比例再保险来分散风险、稳定经营.通过构造鞅过程,运用鞅方法和拉格朗日对偶法求解出最优策略与最优财富.最后进行数值分析,更加直观地解释了各经济参数对财富值和投资策略的影响.This paper introduces the concept of loss aversion in behavioral finance,and studies an optimal reinsurance and investment problem for a loss-averse insurer.Most investors are risk-averse towards gains,but they will change to be risk-seeking when they suffer from losses,so we assume that the insurer’s goal is to chose the optimal strategy to maximize the expected S-shaped utility from the terminal wealth.The surplus process of the insurer is assumed to follow a classical Cramer-Lundberg model and the insurer is allowed to purchase proportional reinsurance.Moreover,the insurer can invest in a risk-free asset and a risky asset.By martingale approach and lagrange dual theory,we derive the optimal strategy.Finally,numerical examples are provided to illustrate the effects of model parameters on the optimal terminal wealth and the optimal strategy.

关 键 词：损失厌恶 比例再保险 鞅方法 S型效用 最优策略 

分 类 号：O22[理学—运筹学与控制论]