风险约束与最优保险:一种更符合投保人期望的保险契约  

Risk Constraint and Optimal Insurance:An Insurance Contract That Better Meets Expectations of the Insured

作　　者：马本江[1] 蒋学海 占金刚 MA Benjiang;JIANG Xuehai;ZHAN Jingang(Business School,Central South University,Changsha 410083,China;Beibu Gulf Ocean Development Research Center,Beibu Gulf University,Qinzhou 535011,China)

机构地区：[1]中南大学商学院,湖南长沙410083 [2]北部湾大学北部湾海洋发展研究中心,广西钦州535011

出　　处：《运筹与管理》2024年第7期208-214,共7页Operations Research and Management Science

基　　金：广西高校中青年教师科研基础能力提升项目(2023KY0418);国家社会科学基金一般项目(23BJY098);广西教育科学规划高校创新创业教育专项课题重点项目(2023ZJY1478);广西高校人文社会科学重点研究基地北部湾海洋发展研究中心创新项目(BHZXSKY2012)。

摘　　要：在保险实践中,投保人往往期望在发生保险事故之后能够获得保险公司的充分赔偿,从而确保他们的实际经济损失被严格控制在预先设定的、可接受的阈值之内。为了满足这类保险需求,本文考虑当投保人损失不大于某个非负特定值时,在Arrow模型的基础上引入投保人的净损失约束以研究投保人的最优保险问题。具体的,本文在投保人的低损失区间而非全损失、高损失区间引入净损失约束,既考虑了投保人效用的帕累托改进,同时又使最优保单含有对投保人合理避险的激励。研究表明:投保人效用最优时,如果低损失区间上的净损失约束不起作用,则Arrow模型解就是本模型的解;反之如果起到作用,则给出了本模型的一个特殊解,并且指出该特殊解存在两个免赔额。此外,投保人的期望效用会随着净损失上限的增大和小损分界点的减小而有所提高,但当净损失上限增大或小损分界点减小到一定程度使得投保人低损失区间上的净损失约束不起作用时,投保人效用达到最大而不再进一步提高。For a long time,an optimal insurance design has always been a hot and difficult issue in insurance theory research,and has attracted widespread attention from theoretical and industrial circles.The pioneering research by Arrow,a Nobel laureate in economics,provides a model basis and research ideas for optimal insurance design.He assumes that risk-neutral insurance companies charge excess premiums in line with the current development level of the insurance market under the principle of expected premiums,while the insured belong to the risk-averse type and have a von Neumann-Morgenstern utility function,and designs insurance products according to the maximum expected utility of the insured.However,Arrow’s research and subsequent related studies ignore the risk constraint needs of the insured.In reality,the insured usually hope to obtain sufficient compensation from the insurance company after an accident and control their own losses within their expected acceptable range.Therefore,if Arrow’s insurance cannot meet the risk constraint needs of the insured,how to design an insurance contract that meets the risk constraint needs of the insured?This issue needs to be further studied.On the basis of the Arrow model,when the loss of the insured is no more than a certain non-negative value,the net loss constraint of the insured is introduced to study the optimal insurance problem of the insured.This is because:(1)Setting the net loss constraint of the insured in the partial range rather than the total loss range is to achieve utility improvement.(2)Setting the net loss constraint of the insured in the low loss range rather than the high loss range,the optimal insurance contract can motivate the insured to avoid risks reasonably.In addition,the constructed model also includes the continuity of the compensation function,which prevents insurance companies from refusing to provide insurance due to concerns about the moral hazard of the insured.According to the research ideas of RAVIV(1979)and GOLLIER(1987),the model is sol

关 键 词：最优保险 风险约束 Arrow模型 免赔额保险 

分 类 号：F840[经济管理—保险]