摘要
在信息部分可观测金融市场中,文章研究了存在股票误价时保险公司时间一致再保险和投资策略.假设保险公司的盈余过程由扩散模型刻画,其可购买比例再保险,并可投资于一个无风险资产,一个市场指数和一对存在误价的股票.这对存在误价的股票的风险溢价是随机且无法直接观测的,但遵循均值回复过程.保险公司的决策目标是终端时刻投资收益最大化的同时最小化投资风险.利用滤波技术和纳什均衡思想,文章得到了时间一致再保险和投资策略的解析式.最后,数值算例表明市场流动性增强会显著增加股票误价的对冲需求;金融市场信息部分可观测导致时间一致投资策略和值函数存在显著的损失;投资期限越长,信息部分可观测导致的保险公司收益损失越大.
In a financial market with partially observable information,this paper investigates time-consistent reinsurance and investment strategies with mispricing for an insurer.Assume that the surplus process of the insurer is described by a diffusion model,allowing the insurer to purchase proportional reinsurance and to invest in a financial market.The insure can invest in a financial market consisting of a riskfree asset,a market index and a pair of mispriced stocks.The risk premiums of this pair of stocks are stochastic and unobservable,but they follow a mean-reverting process.The goal of the insurer is to maximize the expectation of terminal wealth while minimizing the variance of terminal wealth.By virtue of the filtering technique and Nash equilibrium,the analytic expressions of time-consistent reinsurance and investment strategies are derived.Numerical analysis shows that the strengthened market liquidity significantly increases the hedging demand for the mispricing;there is non-negligible information loss on the time-consistent investment strategy and value function due to partial observation in the financial market;the longer the investment horizon is,the greater the profit loss of the insurer caused by the loss of information.
作者
王佩
张玲
范思雨
WANG Pei;ZHANG Ling;FAN Siyu(School of Economics and Trade,Guangdong University of Finance,Guangzhou 510521;Postdoctoral Research Station of Institute of American Studies,Chinese Academy of Social Sciences,Beijing 100720)
出处
《系统科学与数学》
CSCD
北大核心
2021年第7期1834-1855,共22页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金项目(71971070,71601055)
教育部入文社科青年项目(20YJC790139)
广东省基础与应用基础研究基金联合基金项目(2020A1515010419,2020A1515110606)
中国博士后科学基金项目(2018M641594)
广东省普通高校青年创新人才类项目(2019WQNCX090)资助课题
关键词
信息部分可观测
股票误价
再保险与投资
纳什均衡
滤波技术
Partial observation
mispricing
reinsurance and investment
Nash equilibrium
filtering technique
