? Risk exposure:
risk units included in a policy in a particular period.
? Written exposure 已签风险量 ? Earned exposure 已获风险量 ? In-force exposure 有效风险量
已经过去的未 发生的风险
– Unbiasedness 无偏估计 – Asymptotically unbiased 渐近无偏估计 – Consistency 一致估计 – Minimum mean square error 最小均方误差估计
Ch7.2.1 Point estimation
lim
n??
E
????n
?
??
?
?
在保单到期之间都 ? 签单时的风险量
Байду номын сангаас
Ch7.2.1 Point estimation
? Methods of Point estimation
– Moment estimator 矩估计 – Maximum likelyhood estimator 极大似然估计
? Quality of estimation
– Determine the rejection region by percentile
– Calculate the estimator value by sample
– Draw a conclude by check wheter the estimate is in the rejection region or not
? risk units in policy ? premium of each unit
premium of each unit
相当于前一章中的c
? risk frequency of each unit ? risk claim of each unit
Ch7.1 Risk unit and exposure
?
Example: P326 example 12.13
? ? lim Pr
n??
??n ? ? ? ?
?0
MSE??(? )
?
E
?????? ?
?2
?
? ?
Ch 7.2.2 Interval estimation Pr ?L ? ? ? U ?? 1? ?
Ch 7.2.3 Tests of Hypotheses
? Tests of Hypotheses is to test a parameter
equal to (less than or greater than) a given value.
? Steps of the test
– Construct an estimator with known distribution
– Check out the percentile of the known distribution corresponding to the level of confidence
非寿险精算 Actuarial Statistics
Ch7.1 Risk unit and exposure
? Risk Unit basic unit for measuring risk exposure and basic unit for pricing risk premium.
? Risk premium of a policy