Mack
Card Set Information
Author:
Esaie
ID:
33865
Filename:
Mack
Updated:
2010-09-10 14:58:01
Tags:
Exam6 by Esaie
Folders:
Description:
Exam6 by Esaie Mack
Show Answers:
Mack variables
U
: ultimate claims
R
: reserve
C
: claims paid
p
_{i}
: % rpt = 1 / CDF
_{ult}
q
_{i}
: % unrpt = 1 - 1 / CDF
_{ult}
BF, CL & Benktander in Mack's notation
U
_{BF}
= C
_{k}
+ q
_{k}
U
_{0}
U
_{CL}
= q
_{k}
*(C
_{k}
/p
_{k}
)
U
_{GB}
= C
_{k}
+ q
_{k}
U
_{BF}
Mack's theorem 1
Further iteration of BF and GB for an arbitrary starting point U
_{0}
finally leads to CL
MSE of Benktander method
Almost as small as that of the optimal credibility reserve
Smaller than for BF