※ 引述《enter (Johnny)》之銘言：
: There is something wrong with my Chinese system,So I have to
: write in English:
: According to professor Chou's class,we know that:
: NAR = F - PR,
: And you should know F is not the cost of insurance company,but NAR.
: As time increase,the insured pays more money to the insurance company
: and results in less NAR.
: Then since F is constant,so PR gets higher as NAR decreases.That's
: the reason why PR is an increase function of t....
: You should suppose no insured claims their policy,or PR will not increases
: I think I have totally understood the meaning.I hope you do,too.
我覺得迷惑是因為..
PR出現是由於平準的關係..所以產生了初期所繳交的保費大於賠償金*死亡的期望值..
那依照平準的假設..
到達後期應該會有所交的保費少於賠償金*死亡的期望值的時候..
所以此時PR應該成為負值..從而抵銷初期所溢繳的部份...
若是以條件機率解釋..eg..四十歲死亡的機率為q40
E(x)=C1/(1+i)+C2/(1+i)^2+........+Cn/(1+i)^n
C1=F*q40
C2=F*(1-q40)*q41
.
.
.
此時老師說C1<=C2<=C3.........
所以PR節節上升...
就在這裡怪怪的..
因為q41>q40這沒問題，但是機率為小於一大於零的數，
所以（1-q40)小於一...那C2怎麼會大於等於C1....
想來癥結應該在於，為什麼畫起來後面有個三角形可以補前面的溢繳三角形..
但轉化後卻沒有抵銷的效果??
--
........沉寂的房舍因人生而喧嘩
單調的空氣因存在而混亂............
.........車依以我而來
我將踏大步而去.............
--
※ 發信站: 批踢踢實業坊(ptt.csie.ntu.edu.tw)
◆ From: m62022.m6.ntu.e