Risk premium defn:
Expected cost of claims during period for which premiums will apply
o May or may not include allocated loss adjustment expenses (ALAE) or unallocated loss adj. exp. (ULAE)
Office premium defn
Office premium = Risk premium + various loadings
Various loadings include:
- Expense loading
- Profit loading & ROC
- Investment return (negative loading)
- Tax & contingencies (to the extent not allowed for in profits)
Main properties of burning cost approach:
- Burning cost premium is based on aggregate actual cost of claims for a past period
- Expressed as an annual rate per unit of exposure
- Does not use info. about number/frequency/severity of claims
- Estimate of business to be written in the future rating period is not required
Data requirements for RUBCA (rating using burning cost approach):
- Policy data
- Claims data
- Rating factors and exposure measure details
Considerations when RUBCA is employed:
RUBCA uses historical claims experience for pricing BUT:
- Need to estimate outstanding (OS) & IBNR claims; if these claims are not considered, this may lead to underpricing (because only historical reported claims were considered for premium rating)
- Individual case-estimates may not be available from the data
o Run-off triangles may need to be used to estimate outstanding + IBNR claims for classes of business
o These should then be allocated b/w rating groups
Burning cost premium defn:
Cost of claims INCURRED in the past per unit of exposure
What are the alternative formulae for burning cost premium? (hint: Fundamental terms of derivation)
-> (Total claims) / (Total exposure)
* Exposure defined as the product of sum insured and time for which policyholder is exposed to risk (eg. no of years)
-> (Total claims)/(no. of claims) x (no. of claims)/(total exp.)
= avg. claims x avg. frequency of claims
Note: Used when the measure of exposure = policy year
-> (Total claims)/(no. of claims) x (no. of claims)/(total exp.)
= (Total claims)/(no. of claims) x
(no. of policies)/(total exp) x
(no. of claims)/(no. of policies)
= (Total claims)/(no. of claims) -: (total exp)/(no. of policies)
x (no. of claims)/(no. of policies)
= (average claims)/(avg. exp. per policy) x
(avg claim per policy)
—————————————————————————————-Fundamental terms for derivation
- Total claims
- Total exposure
- No. of claims
- No. of policies
What does trending and development of losses concern?
- Adjust claims & exposures to current values (using index of some sort)
- Make assumptions about type of loss / date of occurrence / date of payment (to project claims & exposures into future)
o Tough for RUBCA because likely to just have aggregate claims for a year - Decide how to deal w large & catastrophe claims:
o Leave them in the data (unlikely)
o Truncate claim and spread the excess
o Remove from data and allow for them separately
What are possible trends we allow for in claims & exposure data?
- Inflation
- Changes in business mix
- Legal/court awards
- Changes in terms and conditions, underwriting or claims controls
** these adjustments will be challenging considering with RUBCA we have aggregate claims (not well detailed data). Might have to make assumptions
Developing losses under RUBCA
- Need to allow for fact that previous year’s exposures are incomplete
- Need to develop claims to ultimate allowing for the IBNR component
How to project past exposure to future projection period?
- Base on past exposure, derived ideally using dates on cover, sum insured or premium, rating factor
Considerations
- Can inflation be allowed for up to the present time?
- Can expected inflation be allowed for from now up to when future business will be written?
- Can known past or expected future trends be allowed for? eg. changes in business mix
These considerations depend on:
- Class of business
- Whether data is available to determine these items.
How to project past claims to future projection period?
- Develop the known claims incurred to ultimate claims and allow for IBNR & IBNER
- Apply trends and inflation to the projections from:
o Period of past data to present date
o From present date to future rating period
Advantages & disadvantages of RUBCA:
Advantages:
- Simplicity
- Little data required
- Fast to carry out
- Allows for actual past experience
Disadvantages:
- Difficult to adjust data for inflation, trends, large claims, T&C - may need broad assumptions
- Might understate premium rate especially if claims are not fully developed to ultimate including IBNR
- Very crude approach but might be appropriate for some business including reinsurance, though could underprice risk & make losses
When is it suitable to use RUBCA?
- When there is not enough detailed data to use another more complicated & more credible approach
- Short-tail classes of business with many claims
- For individual commercial risk with many claims e.g. motor fleet, personal accident
