Loss development

Question 1

Estimated ultimate claims from incremental paid claims and development pattern of % paid of ultimate

Answer 1

Add all incremental claims to get latest cumulative paid figure. Then divide by % expected development at latest delay to estimate ultimate.

Question 2

What bias is present when claims data is collected on accident year basis and pattern give was on underwriting basis

Answer 2

Claims patterns by underwriting year develop more slowly than claims by accident year because the measurement of delay includes delay between underwriting and accident - which averages about 6 months

Question 3

Describe the relationship between accident year claims and underwriting claims

Answer 3

Delay between underwriting and accident averages about 6 months. Suppose all the claims come from accident year y. About half of those have come from underwriting year y-1 and have from underwriting year y. So cumulative paid for accident year y consistent half with accident year delay y-1 and half with accident year y

Question 4

Describe a possible method when claims data is collected on accident year basis and pattern give was on underwriting basis

Answer 4

Disregarding half of the last year’s incremental claims to allow for the use of an underwriting year pattern.
Taking averages assumes linearity in development pattern wheras actual pattern is liekly to be concave in the tail.This method likely gives an overestimate but is more accurate than no adjustment.
We also assumes similar volumes in claims across the two year’s - could be untrue could have been more claims in one year than the other.

Question 5

What is the meaning of ultimate claims

Answer 5

Ultimate claims are the limit of claims as delay goes to infinity

Question 6

What data would be needed to construct a model predicting ultimate claims

Answer 6

Paid claims by delay, Fitted model, incurred claims, previous (more developed) years data, underwriters estimates.

Question 7

What are ultimate claims and what are incurred claims to date based on underwriters initial loss ratio, assumed development pattern and premium

Answer 7

Premium * loss ratio = ultimate claims
Ultimate claims estimate by underwriter * Assumed development pattern = theoretical incurred claims to date

Question 8

What is the underwriters approximation of IBNR based on underwriters initial loss ratio, assumed development pattern and premium

Answer 8

Premium * loss ratio = ultimate claims
Ultimate claims*(100%-development pattern)=theoretical IBNR

Question 9

How would underwriter respond to new methods improving on their estimates, which were too low

Answer 9

Unlikely to be happy as an increase in estimates ultimate reflects badly on their underwriting. Underwriter might argue higher than expected payments is an acceleration of what would otherwise have been paid later and therefore the future payments will be lower and their original ultimate still stands.

Question 10

How to compute ultimate losses by BHF method

Answer 10

See according to the fitted pattern/model the % of claims that should be incurred by latest delay by taking incurred/predicted ultimate
This gives a % still left to be incurred - call this b

We do: Underwriters estimated ultimate*b% = IBNR
BHF Ultimate = latest incurred plus estimated IBNR

Question 11

What are some advantages of the BHF method compared to the direct method of using a model to predict ultimate

Answer 11

Takes account of non triangular information(underwriters estimates) - this is very useful for poorly developed years of account where development factor methods can give fluctuating estimates. - underwriter estimates have a stabilizing effect providing estimates have information’s content.
Might make underwriter look better in comparison to direct method - calculate the loss ratio to check.

Question 12

What additional information apart from paid claims triangle and expected future claims would one need to refine an estimate for ultimate claims?

Answer 12

Provisions for notified outstanding claims
Any changes in development patterns by year
Underwriters initial estimates via BHF.

Question 13

Why is a linear relationship between cumulative paid claims and delay unlikely to lead to useful estimates of ultimate claims

Answer 13

Purpose is to estimate ultimate claims by taking the limit for large d - this cannot work for an increasing linear function as the limit will be infinite.

Question 14

What are the boundaries of a model to estimate ultimate

Answer 14

If model is y(d) being the proportion of ultimate by delay d we want an increasing function with y(0)=0 and y(infinite)=1 as all claims must be settled eventually.

Question 15

What is a disadvantages of analyzing paid and incurred claims separately?

Answer 15

In theory paid and incurred claims should converge to the same ultimate limit as all outstanding claims should be settled eventually. If the two claims definitions are extrapolated separately then two different limits might be estimated.

Question 16

Reasons why claims payment may be delayed for years beyond the data of an accident

Answer 16

Delay in determining the accident has occurred ex: exposure to chemicals or injury delay
Delay in the injured party reporting a loss to the insured
Delay in insured reporting to insurer
Delay from insurer validating the claim
If the claim is disputed there may be delayed waiting for court appointments
Court appeals
Some insurance claims are paid in installments over a number of months or years ex: cost of care.

Question 17

Assumptions of the chain ladder method to calculate reserves

Answer 17

Same development pattern applies to each accident year - assumes claims reporting and handling delays are consistent between years.
Assumes first year is fully developed and that there is zero IBNR. This is unlikely to be true - An IBNR factor should usually b applied to allow for further development.
Inflation adjusted chain ladder: assumption that claims are paid at the end of june

Question 18

What is involved in the ACPC method - is it more accurate than the chain ladder method

Answer 18

Average cost of claims method involved projecting, separately the claims numbers and the average claim amount.
This can improve accuracy is separate trends in claim numbers and average claim size can be identified and projected separately. Accuracy may be further improved by identifying and treating separately any individual large claims so that they do not distort observed development patterns.

Question 19

How does the variance of ultimate claims change across the different origin years in the loss triangle

Answer 19

Predictive variance is much higher for the later years because the data is less developed and so more uncertainty remains.