考虑模型不确定性的中国死亡率预测——基于贝叶斯模型平均方法

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。     

我国车险市场道德风险的博弈分析

车险已成为我国产险的龙头险种,但由于信息不对称,车险市场道德风险已严重制约产险业的发展。各利益主体为自身效用最大化不断博弈的最终结果,使得车险市场整体运行效率大打折扣。本文运用博弈论的研究方法,通过构建博弈模型,对投保人、保险人、保险代理人以及汽车修理商四方行为主体的道德风险进行博弈分析,探寻其最优策略,并给出对策建议。     

保险欺诈防范方法之八：巧用免赔额

从理论上讲，保险人和投保人总是处于欺诈和反欺诈的博弈之中，欺诈有收益也有成本，反欺诈需要成本支出也能获得收益。按照经济人的假定，保险人和被保险人在不完全信息的动态博弈中会达到一个均衡，在这个均衡点上双方的策略处于最优，这时的保险合同也是最优保险合同：部分保险。基于保险人和投保人双方最优博弈策略的保险合同形式不可能是足额保险，而只能是部分保险，其原理在于使得投保人和保险人共同承担保险标的的风险损失，以此来遏制和减少投保人的欺诈行为，一般而言，投保人承担的部分越大，其实施保险欺诈的动因和可能性就越小。这一原理在保险产品设计中的应用就是大量采用绝对免赔额、相对免赔额（率）和不足额保险三种方式。     

车险免赔可否多样化

在车险业务管理中，保险公司为小额赔案投入了大量的人力和物力，通过建立多样化的免赔额(率)，不但可以为投保人减少一部分费用开支，而且可以使保险公司从车险小额赔案的繁琐工作中解脱出来，为客户提供更多的优质服务。     

车险市场化步伐不宜过快

长期以来,我国的机动车辆保险一直处于严格的监管之下,随着市场的发展,近两年车险市场化经营的呼声越来越高.实行市场化经营的有利之处主要体现在以下几方面:一是通过市场机制的自发调节,有利于营造更加公平、合理、有序的市场环境,促进车险市场的健康发展.二是有利于给保险人更多自由经营的空间,促使其加强产品创新,给投保人更多比较与选择的机会.     

几个保险法制度的法律经济学分析

保险市场中危险的可保性、道德危险和逆向选择问题都涉及到经济学中的激励问题,以及成本收益问题。想要很好地解决以上问题需要我们制定出一些行之有效的激励措施对被保险人的行为加以引导。而经济学的分析方法对于追求利润最大化的保险人和最求效用最大化的投保人都非常的适用。     

关于免赔额——财产险业务学习笔记

免赔额是指保险人根据保险合同的约定作出赔付之前,由被保险人自己承担的损失额度。所谓免赔额,《中国保险辞典》解释为：保险人对某种保险标的规定在一定限度内的损失不负赔偿责任的金额。保险人对各类标的规定不同的免赔额。保险人在计算赔款时,凡损失超过这个免赔额而进行全部赔偿的叫“相对免赔额”,只赔偿超出免赔额那一部分的叫“绝对免赔额”。     

机动车辆保险合同条款比较研究

为履行我国加入WTO的承诺, 国家保险监管部门宣布:自2003年1月1日以后,由各保险公司自行制定机动车辆保险条款和费率,由此我国车险市场经历了一场巨大的变革,揭开了车险条款费率市场化的序幕。各保险人根据自身的车险经营状况分别制定了自己的车险条款和费率规章。综观各保险人自行制定的车险条款,在条款的结构、责任范围的界定、     

保险市场逆向选择的信号传递博弈研究

在保险市场中,投保人比保险人更了解自己的风险状况,保险双方之间的这种信息不对称难以避免地会产生逆向选择问题,于是在保险人混同定价的情形下,低风险投保人要承受过高的费率而受损,高风险投保人因保险成本过低而削弱控制风险的激励,导致整个市场资源配置低效甚至因逆向选择螺旋而崩溃。通过引入信号传递机制来实现保险市场的分离定价,从...     

论我国保险市场的不完善

由于中国的保险业建立较晚而发展有限,因而在这个新兴的业务市场中尚存在很多不完善的地方,主要体现在市场参与者的产权缺位与不成熟、信息披露机制的不完善等方面。一、市场参与者的产权缺位与不成熟保险市场的主体主要是保险人和投保人,在此首先对保险人问题进行分析。在我国     

On the Theory of Rational Insurance Purchasing: A Note

The authors consider the optimal amount of insurance purchased by an individual who behaves according to the Hurwicz criterion of choice under uncertainty. Their results are compared with earlier results obtained in alternative frameworks (expected utility maximization and Savage's regret criterion). It is shown that a positive amount deductible is often suboptimal.     

The Incentive Effects of Increasing Per-Claim Deductible Contracts in Automobile Insurance

A new rating system of automobile insurance for vehicle damage in Taiwan was launched in 1996, introducing a deductible that increases with the number of claims. In this article, we provide a theoretical rationale for the existence of an increasing per‐claim deductible system and show that the new system is most likely an optimal choice for those insured who tend to have lower claims probability when incentives are present. Using a unique dynamic data set, we are able to conduct a natural experiment to examine the incentive effects (both positive and negative) by looking at the change in claim tendency before and after switching between two deductible plans: an increasing per‐claim deductible and a zero deductible. Our results provide direct evidence of the effects of deductible structures on claim behavior.     

On Compulsory Per-Claim Deductibles in Automobile Insurance

The purposes of this paper are to analyze the theoretical characteristics of the compulsory deductible system and to verify the rationality of an increasing per-claim deductible in automobile insurance. We derive the optimal variable per-claim deductible by assuming the insurers are financially balanced and the expected utility of the insured is maximized in the absence of moral hazard. Our result suggests that a variable per-claim deductible increasing with the number of claims per year is not optimal. Instead, deductibles should be charged in a decreasing rate forming a second-best solution.     

Optimal insurance contract and coverage levels under loss aversion utility preference

This study develops an optimal insurance contract endogenously and determines the optimal coverage levels with respect to deductible insurance, upper-limit insurance, and proportional coinsurance, and, by assuming that the insured has an S-shaped loss aversion utility, the insured would retain the enormous losses entirely. The representative optimal insurance form is the truncated deductible insurance, where the insured retains all losses once losses exceed a critical level and adopts a particular deductible otherwise. Additionally, the effects of the optimal coverage levels are also examined with respect to benchmark wealth and loss aversion coefficient. Moreover, the efficiencies among various insurances are compared via numerical analysis by assuming that the loss obeys a uniform or log-normal distribution. In addition to optimal insurance, deductible insurance is the most efficient if the benchmark wealth is small and upper-limit insurance if large. In the case of a uniform distribution that has an upper bound, deductible insurance and optimal insurance coincide if benchmark wealth is small. Conversely, deductible insurance is never optimal for an unbounded loss such as a log-normal distribution.     

Disappointment and the Optimal Insurance Contract

This paper studies the optimal insurance contract under disappointment theory. We show that, when the individuals anticipate disappointment, there are two types of optimal insurance contract. The first type contains a deductible and a coinsurance above the deductible. We find that zero marginal cost is just a sufficient but not a necessary condition for a zero deductible. The second type has no deductible and the optimal insurance starts with full coverage for small losses and includes a coinsurance above an upper value of the full coverage.     

General Insurance Deductible Ratemaking

Insurance claims have deductibles, which must be considered when pricing for insurance premium. The deductible may cause censoring and truncation to the insurance claims. However, modeling the unobserved response variable using maximum likelihood in this setting may be a challenge in practice. For this reason, a practitioner may perform a regression using the observed response, in order to calculate the deductible rates using the regression coefficients. A natural question is how well this approach performs, and how it compares to the theoretically correct approach to rating the deductibles. Also, a practitioner would be interested in a systematic review of the approaches to modeling the deductible rates. In this article, an overview of deductible ratemaking is provided, and the pros and cons of two deductible ratemaking approaches are compared: the regression approach and the maximum likelihood approach. The regression approach turns out to have an advantage in predicting aggregate claims, whereas the maximum likelihood approach has an advantage when calculating theoretically correct relativities for deductible levels beyond those observed by empirical data. For demonstration, loss models are fit to the Wisconsin Local Government Property Insurance Fund data, and examples are provided for the ratemaking of per-loss deductibles offered by the fund. The article discovers that the regression approach is actually a single-parameter approximation to the true relativity curve. A comparison of selected models from the generalized beta family discovers that the usage of long-tail severity distributions may improve the deductible rating, while advanced frequency models such as 01-inflated models may have limited advantages due to estimation issues under censoring and truncation. In addition, in this article, models for specific peril types are combined to improve the ratemaking.     

The Demand for Insurance With an Upper Limit on Coverage

The demand for insurance is examined when the indemnity schedule is subject to an upper limit. The optimal contract is shown to display full insurance above a deductible up to the cap. Some results derived in the standard model with no upper limit on coverage turn out to be invalid; the optimal deductible of an actuarially fair policy is positive and insurance may be a normal good under decreasing absolute risk aversion. An increase in the upper limit would induce the policyholder with constant absolute risk aversion to reduce his or her optimal deductible and therefore this would increase the demand for insurance against small losses.     

The comparative statics of deductible insurance in expected- and non-expected-utility theories

This paper identifies comparative statics results for insurance contracts that distinguish between various models of decision making under risk—specifically, expected utility, rank-dependent expected utility, and weighted utility. Insurance contracts offer full coverage above a deductible. Firms offer premium schedules that give the premium charged as a function of the deductible; households choose both an insurance company and a deductible to maximize utility. A competitive equilibrium requires zero expected profit for firms. We identify changes in the distribution of losses such that the optimal deductible increases for utility representations in a particular class but decreases for some representations outside that class. We give results both for the demand for insurance, as well as for the equilibrium contract.     

An Empirical Analysis of the Effects of Increasing Deductibles on Moral Hazard

Using information on timing and number of claims in a unique data set pertaining to comprehensive automobile insurance with the increasing deductible provision in Taiwan, the authors provide new evidence for moral hazard. Time-varying correlations between the choice of the insurance coverage and claim occurrence are significantly positive and exhibit a smirk pattern across policy months. This empirical finding supports the existence of asymmetric information. A subsample estimation depicts insured drivers' significant responses to increasing deductibles, which implies the existence of moral hazard. According to the probit regression results, the increasing deductible makes policyholders who have ever filed claims less likely to file additional claims later in the policy year. The empirical findings strongly support the notion that the increasing deductible provision helps control moral hazard.     

A Note on Deductible Insurance and Production

This paper examines the optimal production decision of a firm facing revenue risk. We show that the purchase of actuarially fair deductible insurance unambiguously induces the firm to produce more if the firm is not only risk averse but also prudent. If the firm's perferences satisfy constant absolute risk aversion, buying actuarially unfair deductible insurance unambiguously enhances production should the positive loading factor be sufficiently small. When there are moral hazard problems in that the firm's output cannot be contracted upon, we show that the purchase of actuarially fair deductible insurance unambiguously induces the firm to produce more if the firm's utility function is quadratic.