无赔款优待系统下考虑损失额的最优索赔策略  

Optimal Claiming Strategies in Relation to Losses in NCD Systems

作　　者：张连增[1] 董舒婷 

机构地区：[1]南开大学金融学院,天津300350

出　　处：《保险研究》2017年第5期34-42,共9页Insurance Studies

基　　金：国家自然科学基金(No.71271121;No.71401041)的资助

摘　　要：无赔款优待系统是车险定价中的基本工具。在实务中,只有当发生的损失较大时,投保人才提出索赔,此时损失由保险人承担,但索赔可能会导致未来保费的上升。当发生的损失较小(或没有损失时),投保人不提出索赔,此时损失由投保人承担,无索赔可能会导致未来保费的下降。因此存在损失临界值(称为隐含免赔额),使得投保人未来各年度保费和自行承担损失的现值最小。最优索赔策略等价于各个保费等级对应的损失临界值。最后,本文使用我国2015年商业车险费率改革后的有关数据,分别在损失额服从指数分布和伽马分布的假设下,计算出各保费等级的隐含免赔额,并定量分析在指数分布假设下不同贴现率对隐含免赔额和无索赔概率的影响。No-Claim Discount （NCD） is a basic component in auto insurance pricing. From the perspective of the insureds, only when the loss is big enough, will they claim for the loss and get reimbursement as well as a premium downgrading. Conversely, when the loss is small or nil, the insureds tend not to lodge the claim, and they suffer the loss but get premium upgrading. This gives rise to some loss threshold, called implied deductible, which minimizes the present value of future claims and premiums. An optimal claiming strategy for a driver is hereby given by a collection of implied deductibles, associated to all the premium levels. Finally, based on the data after the retorm pilot of Chinese motor vehicle rate making in 2015, and under the assumption that the loss followed exponential and Gam- ma distributions, we calculated the implied deductibles of all premium levels respectively, and analyzed the relationship between discount rate and implied deductibles and the non-claiming probability quantitatively under exponential distribution.

关 键 词：无赔款优待系统 最优索赔策略 马尔可夫链 

分 类 号：F840.65[经济管理—保险]