Reported Claims
Reported Claims = Paid Claims + Case Outstanding
Unpaid Claims (2 formulas)
Unpaid Claims = Case Outstanding + IBNR (Broad Def.)
= Ultimate Claims - Paid Claims
IBNR (Broad Definition) (sum of 4 elements)
- Pure IBNR
- Provision for claims reported but not recorded
- IBNER (Adj to Case Reserve)
- Estimate for reported claims
Ultimate Claims
= Paid Claims + Case Outstanding + IBNR
= Reported Claims + IBNR
3 Approaches to Select Tail Factors
- Industry benchmark development factors
- Curve fitting to extrapolate the tail factors (Exponential decay)
- Utilizing reported-to-paid ratios at the latest observed paid development period
Assumptions of development method (3)
- Claims recorded to date will continue to develop in a similar fashion in the future
- For AY not fully developed, claims observed thus far give us relevant information on claims that give us relevant information on claims that have yet to be observed
- Throughout policy period :
3.1. Consistent claims processing (Settlement rate & case reserve adequacy)
3.2. The mix of claims is stable
3.3 Policy limits and deductibles are stable (if any)
3.4 Reinsurance retention limits are stable (if any)
Situations in which the development method works well (3)
- Large amount of credible historical claims data available
- High-frequency, low severity lines with stable and timely reporting of claims
- When the presence or absence of large claims does not greatly distort the data
For development method : Impact of speedup in settlement rate
Paid Claims : Overestimates development factors dans ultimate claims
Reported Claims : No effect
For development method : Impact of Increase in case reserve adequacy
Paid Claims : No effect
Reported Claims : Overestimates development factors and ultimate claims
For development method : Impact of increase in freq and/or sev
Claims increase, but development factors are unaffected
For development method : Impact of increase in exposures
Claims increase, but development factors are unaffected if the average accident date is held constant
For development method : Impact of
Underestimates development factors and ultimate claims
For development method : Impact of change in product mix
Development factors change to reflect the new mix
Expected Claims Method : Key Assumptions (2)
- Claims paid to date for a given AY provide no useful information on future claims for that AY
- The actuary can determine a reasonable expected claims ratio
Uses of expected claims method
- New line of business or territory
- Operational or environmental changes makes historical data unreliable
- Development factors for early maturities are highly leveraged
- Data is limited or unavailable
Advantage (1) and disadvantage (1) of expected claims method
Advantage : Not subject to data uncertainties, gives very stable ultimate claims estimate
Disadvantage : Not responsive to recent claims experience
For expected claims method : Impact of speedup in settlement rate
Paid : Overestimates ultimate claims, but not as much as the development method would
Reported : No impact
For expected claims method : Impact of increase in case reserve adequacy
Paid : No impact
Reported : Overestimates ultimate claims, but not as much as the development method would
For expected claims method : Impact of increase in freq/sev
The EC method accounts for changes unless they occurred within the most recent year
In that case, ultimate claims would be underestimated
For expected claims method : Impact of increase in exposures
No effect, as long as average accident date is held constant
For expected claims method : Impact of average accident date shifts forward
Underestimates ultimate claims, but not as much as development method
For expected claims method : Impact of change in product mix
Impacted if segments changing have different development patterns or different ECR
Main assumption of B-F method
Unreported/Unpaid Claims will develop based on expected claims
Situations in which B-F works well (3)
- When there are random fluctuations or large claims at early maturities
- When entering a new line of business
- When estimating ultimates at early maturities for long-tailed lines of business
