TPM construction

[Priyanka Malhotra]

Hi , my query is related to question below

An insurer operates a simple no claims discount system with 5 levels: 0%, 20%, 40%, 50% and 60%. The rules for moving between levels are: An introductory discount of 20% is available to new customers. If no claims are made during a year the policyholder moves up to the next discount level or remains at the maximum level. If one or more claims are made during the year, a policyholder at the 50% or 60% discount level moves to the 20% level and a policyholder at 0%, 20% or 40% moves to or remains at the 0% level. The full annual premium is £600. When an accident occurs, the distribution of loss is exponential with mean £1,750. A policyholder will only claim if the loss is greater than the extra premiums over the next four years, assuming no further accidents occur
(i) For each discount level, calculate the smallest cost for which a policyholder will make a claim.

for constructing the TPM why do we not divide the 0% discount as follows:

0% if new customer if claims-->0%-->20%-->40%-->50%, if no claim : 40%-->50%-->60%-->60%

0% if old (or claimed before/just had a claim) claims-->0%-->20%-->40%-->50%, if no claim : 20%-->40%-->50%-->60%


whereas in question below we have considered 0% new customer and 0% just had a claim, given assuming no further accident is consistent in both cases

The no claims discount (NCD) system operated by an insurance company has three levels of discount: 0%, 25% and 50%. If a policyholder makes a claim they remain at or move down to the 0% discount level for two years. Otherwise they move up a discount level in the following year or remain at the maximum 50% level. The probability of an accident depends on the discount level: Discount Level Probability of accident 0% 0.25 25% 0.2 50% 0.1 The full premium payable at the 0% discount level is 750. Losses are assumed to follow a lognormal distribution with mean 1,451 and standard deviation 604.4. Policyholders will only claim if the loss is greater than the total additional premiums that would have to be paid over the next three years, assuming that no further accidents occur. (i) Calculate the smallest loss for which a claim will be made for each of the four states in the NCD system

Thanks in advance

Priyanka

 

[Andrew Martin]

Hello

For part (i), it doesn't seem relevant to me whether a customer is new or not, it just asks for the minimum cost for policyholders on each discount level to make a claim.

If someone is currently at 0% then the options are (assuming no claims in next four years):
1. Claim and the path is then 0%(current state)-0%-20%-40%-50%
2. Don't claim and path is then:
0%(current state) - 20%-40%-50%-60%

From looking at the second question, the reason the approach appears different is because policyholders who claim go to 0% for two years. So we have to distinguish between policyholders who have just moved there or who have been there a year already.

Hope this helps!

Andy

 

[Andrew Martin]

Also, for the second example, if someone is a new customer at 0% then presumably they go up to the next level if they don't have a claim and so again need to be differentiated from those policyholders just moving to 0% and so have to stay there two years.