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Stewert: Reserving workers compensation High deductibles (expected losses…
Stewert
: Reserving workers compensation High deductibles
Hight deductibles
Given Workers compensation's typical long-tailed nature, actual experience over high deductibles emerges slowly over time
Advantages of high deductible programs
Achieves price flexibility while passing additional risk to larger insureds
Reduces residual market charges and premium taxes
Gives cash flow advantages to insured
Provides incentive for insureds to control losses while protecting them from large losses
Allows “self-insurance” without subjecting insured to demanding state requirements
Adjusting the deductible by indexing keeps the proportion of deductible-to-excess losses constant about the limit from year to year, in theory at least
A constant deductible over time usually implies increasing excess losses
Development for loss excess of aggregate limits decreases more rapidly over time with smaller deductibles than larger ones. This is expected since most of the later development occurs in the layers above the deductible limits, which is not covered by the aggregate
Calculating excess losses via implied development
Steps
1.Develop full coverage losses to ultimate
2.Develop losses under the deductible to ultimate .Apply development factors reflecting various inflation to index deductible limits
3.Determine ultimate excess losses by subtracting (2) from (1)
Advantages
Provides an estimate of excess losses at early maturities even when excess losses have not yet emerged
Development factors for limited losses are more stable than those determined for losses above the deductible
Estimating deductible losses helps determine the asset represented by revenue collected from the application of a loss multiplier to future losses
Disadvantage
Does not explicitly reconize excess loss devlopment
Calculating excess losses via direct devlopment
Steps
Directly developping excess loss development factors
Advantage
Explicitly focuses on excess development
Disadvantages
Factors tend to be quite leveraged and extremely volatile, making selection difficult
If excess losses have not actually emerged at any particular stage of development, it is not possible to get an estimate ot the required liability
key definitions
(see formulas sheet)
C
counts
S
severity
R
severity relativity
L
limit
Inverse power curve
Develop limites losses to ultimate
Usefull when there are no observed osses from which to calculate CL factors
Advantage
Consistent for each limit and produces uniformly decreasing tail factors
Disadvantage
Bias exists due to extending each limit to the same maturity . The bias being significant or not is still an open issue
Distributional model
Models the development process by determining distribution parameters that vary over time. Once the parameters are determined, we can calculate severity relativities at different maturities, which allows us to calculate development factors
Can be fit via
Method of moments
Maximum likelihood
minimizes the chi-square between the actual and expected severities
Advantages
Consistent LDFs
Alows interpolation among limits and years
Service revenu
steps to calculate the asset
1.Determine ultimate deductible losses at the account level
2.Subtract ultimate losses excess of aggregate limits from ultimate deductible losses
3.Apply the selected loss multiplier to the difference determined in step 2 to determine ultimate recoverables
4.Determine the total asset by subtracting any known recoveries from the estimated ultimate recoverables and aggregate results for all accounts
Idea
The revenue associated with servicing claims under a high deductible program is reflected on the asset side of the balance sheet
expected losses excess of the aggregate limit using Table M
1.Determine the expected losses limited by the occurrence deductible at the given maturity
2.Calculate the per occurrence charge
3.Calculate the adjustment factor
4.Calculate the adjusted limited losses by multiplying the ultimate unlimited losses by the adjustment factor. Use this amount to determine the Expected Loss Group (ELG)
5.Calculate the entry ratio
6.Determine the insurance charge based off the ELG and entry ratio
7.Calculate expected excess of aggregate loss at maturity t