咨询：关于非寿险精算中索赔频次的问题

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各位：
       最近在看非寿险精算书的时候，对于信度保费这一块有些困惑，有两个问题：
1、当计算完全可信的索赔频次时，如1082次索赔就可当做完全可信，这里面怎么没有说期限呢？这个1000多次是一年中的索赔次数，还是三年的，或者五年的，或者十年的呢？
2、如果对于某个具体业务，比如其3-5年都没有出险，那么我们是按该业务所属风险类别的平均费率来收费（因为个体自身风险的索赔频次为0，所以置信度为0=0/1082，假设1082次就可信的情况下），还是折扣费率呢？折扣费率的标准是什么，有没有严格的数学理论来做依据？

忘各位不吝赐教，谢谢！

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关键词：非寿险精算 寿险精算 非寿险 数学理论 索赔次数 精算 寿险

1. To calculate credibility premium, you first have a loss random variable, say X. X has already encoded the time span you mentioned. For example, X is the number of claims of a policyholder IN ONE YEAR. Please read more examples in your text.
2. First, partial credibility factor is not 0/1082, it should be sqrt(0/1082), although the figures are the same. Back to the question, you are right if you base credibility factor on the number of CLAIMS. Then for full credibility, you charge the policyholder the manual premium (expectation). This makes sense in the way that the policyholder has never told you his/her loss experience (or you never know since he/she does not CLAIM). However, if you calculate credibility based on number of year, say, in the i-th year the claim is X_i, and if the policyholder qualifies for some partial credibility factor Z say after 5 years, then the new premium should be Z*X_bar + (1-Z)*mu = (1-Z)*mu if X_bar is 0. Then there is a discount of Z, coinciding with your intuitions. Note that credibility factor Z would be different if you calculate using different random variables (e.g. number of losses, number of claims, number of policy years, amount of losses, amount of claim payments). It is possible that a policyholder qualifies for full credibility under a certain method but not under another.
By the way, credibility theory (expecially classical) is not very rigorous in mathematics. It does employs maths extensively, but it is rather a practical rule-of-thumb technique rather than a logically-sound theory. Please refer to Page 557 of Loss Model 3rd edition.

KevinOu 发表于 2012-11-4 01:00
1. To calculate credibility premium, you first have a loss random variable, say X. X has already enc ...

非常感谢你的回答和解释。不过我还是有些疑问：
1）就商业财产保险，对于某类客户，如电子元器件生产企业，用索赔频次来当做变量的话，一年的期限肯定是不够，因为可能一年的保单数只有200张，索赔频次的话，更不可能有多少；那么，我们就要看5-10年的数据了，索赔频次可能够完全置信的标准。不过，问题也来了，这种情况是既有时间作为变量又有索赔频次作为变量，如何来确定谁更可信呢？或者如何将两者结合起来呢？
2）非寿险，尤其是商业财产险这一块，如何将数学理论应用在定价中？有没有比较好的书推荐一下？因为目前的精算都是偏重于寿险这一块，即使是非寿险，也是偏向于车险和意外健康险，而对于需要更多专业技术知识支持的物质损失财产险，缺没有多少提及。包括SOA也是侧重寿险，CAS的内容也没对火灾保单等做多少涉及。
谢谢！