CENTRAL RATING
This is a
method I have had developed to modify the experience rating, retrospective
rating and schedule rating to the greatest accuracy. It has the same assumption
of the experience rating, retrospective rating and schedule rating, which states
that the loss experience of any particular insured’s differs. The Central
Rating System is being developed to modify the accuracy in comparison
with the experience rating, retrospective rating and schedule rating system.
The Central
Rating can be widely used in much similar areas to retrospective rating
and experience rating, which include large organization in workers compensation
insurance, general liability insurance, burglary insurance, auto liability insurance
and physical damage insurance.
In Central
Rating System, the percentage of next premium(NP) to be applied on a payment of next loss(NL) is changed by the percentage ∆r and is calculated as;
∆r=(1-NP/PP)/αi
Where;
∆r=Rate change
PP=Present premium
NP=Next premium
αi=Credibility coefficient per risk(or
insured)
The next
premium(NP)is computed as;
NP=αiXim+βiXm
The
credibility coefficient per risk (or insured), αi and total
credibility coefficient βi is given as;
αi=[ZiXim
+ (1-Zi)Xm]/2Xim
βi=[ZiXim
+ (1-Zi)Xm]/2Xm
EXAMPLE
You are
given the folling data on large business policyholders:
i)Losses for
each employee of a given policyholder are independent and have a common mean
and variance.
ii)The
overall average per employee for all policyholders is 20.
iii)The
variance of the hypothetical mean is 40.
iv)The
expected value of the process variance is 800.
v)The
following experience is observed for a randomly selected policyholder:
Year
|
Average Loss Per Employee
|
Number of Employees
|
1
|
15
|
800
|
2
|
10
|
600
|
3
|
5
|
400
|
a) Determine the Central Credibility
premium per employee for the next policy.
b) What change of percentage should be
applied on payment of the next loss per
employee if the present premiums is 10.25?
SOLUTION
In part(ii) you are given µ=20.
In part(iii) you are given VHM=40.
In part(iv) you are given that EPV=800.
Therefore; k=VHM/EPV=200. Then,
Xm=[800(15)+600(10)+400(5)]/1800=11.111
Z=1800/(1800+200)=0.9
α=0.540
β=0.300
a)NP=0.54(11.11)+0.30(20)=11.555
b)∆r=(1-11.555/10.25)=-0.23577
Hence, a change of 23.58% is needed for the payment of 11.56.
REFERENCE
William(Me). Adongo Ayine Diary(Weblog).
“Central Credibility”
