投保人高损失区间存在净损失约束的最优保险设计  

Optimal Insurance with Net Loss Constraint in the High-loss Range of the Insured

作　　者：马本江[1] 蒋学海 MA Benjiang;JIANG Xuehai(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3期15-21,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);国家社会科学基金资助项目(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：在不完全保险情形下,投保人通常期望出险后能够获得保险公司足够的赔偿而将自己的实际损失控制在一定的范围内。为了满足这类投保人的需求,本文引入了投保人的净损失约束,研究在该约束下投保人的最优保险问题。研究表明:如果Arrow模型的解满足该约束,本模型的解与Arrow模型解一致,最优保单是有且仅有一个免赔额的部分保险契约,否则最优保单将存在两个免赔额。投保人效用最优时,本模型在应对高损时所提供的赔付水平始终不低于Arrow模型,而本模型在应对低损时对于IARA(DARA/CARA)型投保人所提供的赔付水平依次要低于(高于/等于)Arrow模型。此外,投保人的期望效用将随着其净损失上限的提高而逐渐增大,直到Arrow模型的解满足该约束时其效用达到最大。Optimal insurance design has always been a hot and difficult issue in insurance theory research.The Arrow model,as a classical model to study the insured’s optimal insurance problem,has been widely used in theoretical and practical circles.Since the Arrow model was put forward,the improvement and optimization around it have never stopped.The improvement and optimization does not mean the utility improvement in information economics,but the design of a more realistic and reasonable insurance model to fully reflect the actual needs of the insured,so as to improve their enthusiasm for purchasing insurance.However,the existing research rarely pays attention to the need of the insured’s risk constraint,and cannot guarantee the expected compensation level of the insured.In the case of incomplete insurance,the insured usually hopes to get enough compensation from the insurance company after loss occurs,so that their actual loss can be controlled within the expected acceptable range,which will be more in line with their original intention of insurance purchase for risk transfer and the types of risk avoidance of most insured.Therefore,this paper intends to set the insured’s risk constraint conditions on the basis of the Arrow model,and study the optimal insurance problem with net loss constraint in the high loss interval of the insured.The designed insurance contract can effectively meet the needs of the insured’s risk constraint and deepen the social management function of insurance transfer risk.Therefore,this study is of far-reaching significance not only for the theoretical expansion of the Arrow model,but also for the long-term development of the insurance market.Firstly,the model is solved from fixed premium to general premium.It is pointed out that if the solution of the Arrow model satisfies the net loss constraint of the insured,the solution of this model is the same as that of the Arrow model,and the optimal policy is a partial insurance contract with only one deductible.Otherwise,the model will have a

关 键 词：最优保险问题 净损失约束 Arrow模型 期望效用 

分 类 号：F840[经济管理—保险]