Loss development Flashcards
Estimated ultimate claims from incremental paid claims and development pattern of % paid of ultimate
Add all incremental claims to get latest cumulative paid figure. Then divide by % expected development at latest delay to estimate ultimate.
What bias is present when claims data is collected on accident year basis and pattern give was on underwriting basis
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
Describe the relationship between accident year claims and underwriting claims
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
Describe a possible method when claims data is collected on accident year basis and pattern give was on underwriting basis
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.
What is the meaning of ultimate claims
Ultimate claims are the limit of claims as delay goes to infinity
What data would be needed to construct a model predicting ultimate claims
Paid claims by delay, Fitted model, incurred claims, previous (more developed) years data, underwriters estimates.
What are ultimate claims and what are incurred claims to date based on underwriters initial loss ratio, assumed development pattern and premium
Premium * loss ratio = ultimate claims
Ultimate claims estimate by underwriter * Assumed development pattern = theoretical incurred claims to date
What is the underwriters approximation of IBNR based on underwriters initial loss ratio, assumed development pattern and premium
Premium * loss ratio = ultimate claims
Ultimate claims*(100%-development pattern)=theoretical IBNR
How would underwriter respond to new methods improving on their estimates, which were too low
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.
How to compute ultimate losses by BHF method
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
What are some advantages of the BHF method compared to the direct method of using a model to predict ultimate
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.
What additional information apart from paid claims triangle and expected future claims would one need to refine an estimate for ultimate claims?
Provisions for notified outstanding claims
Any changes in development patterns by year
Underwriters initial estimates via BHF.
Why is a linear relationship between cumulative paid claims and delay unlikely to lead to useful estimates of ultimate claims
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.
What are the boundaries of a model to estimate ultimate
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.
What is a disadvantages of analyzing paid and incurred claims separately?
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.