ADONGO'S CENTRAL RATING THEORY

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)/α_i

Where;

∆r=Rate change

PP=Present premium

NP=Next premium

α_i=Credibility coefficient per risk(or insured)

The next premium(NP)is computed as;

NP=α_iX_im+β_iX_m

The credibility coefficient per risk (or insured), α_i  and total credibility coefficient  β_i  is given as;

α_i=[Z_iX_im + (1-Z_i)X_m]/2X_im

β_i=[Z_iX_im + (1-Z_i)X_m]/2X_m

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,

X_m=[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”