Aggregate Excess Loss Cost Estimation Flashcards
Advantage of using vertical slices
Size method
More intuitive
Advantage of using horizontal slices
Layer method
Faster if calculating XS losses for multiple limits
Entry ratio
Ratio of actual loss to expected loss
Used to adjust for size of risk
Table M charge, definition
Expected percent of losses > rE
Table M savings, definition
Expected percent of losses < rE
Table M process
Find all given r
Ø(ri) = (ri+1 - ri) * % of risks above r
Ø(rmax) = 0
Savings = Ø + r - 1
Why Table M charge columns would be needed for different risk sizes
Variance of aggregate loss distribution will vary by risk size
Larger size, less variance
Diagram representing Table M charge and savings
Formulas for Table M charge and savings, continuous distribution
First and second derivatives of Table M charge and savings
What happens to charge and savings as entry ratio and risk size go to infinity
Variance in ratios goes to zero, so curve will flatten
Charge becomes max (0, 1 - r)
How an error in estimation of expected losses impacts insurance charge
% error is greatest for large policies with high r
$ error is greatest for large policies with low r
Adjusted expected losses for a risk
Expected losses x State Hazard Group Differential
Purpose of State Hazard Group Differential
Some policies of same size are riskier than others
Differential adjusts expected losses to match those of a different size but same distribution shape
How NCCI moving to expected claim counts (instead of losses) will change risk mapping
No longer need to update for inflation
Riskier groups will lower expected # of claim counts, so variance of aggregate distribution would be higher
If severity distribution differs in scale only, it will be effective
Guaranteed Cost Premium
GCP = (e + E[A])T
Expected retrospective premium
E[R] = (B + c(E[A] - I))T
Basic Premium formula
B = e - (c - 1)E[A] + cI
Expense component of basic premium
e - (c - 1)E[A]
Value, or charge difference
Only true if the plan is balanced
Entry difference
Always true
Limited Table M entry ratios
r* = limited losses / expected limited losses
Basic premium with limited Table M
BLM = e - (c - 1)E[A] + c(ILM + kE[A])
k = 1 - expected limited losses / expected unlimited losses
Excess Loss Pure Premium Factor (also called excess ratio)
k = 1 - expected limited losses / expected unlimited losses
Balance equations, limited Table M
Same as Table M balance equations but with expected limited loss on the denominator
Relationship between expected losses and insurance charge
E[L] = E[A] - I
ICRLL definition
Insurance Charge Reflecting Loss Limitation
ICRLL approximation, adjusted expected losses
Adjusted Expected Loss = E[A] x SHG differential x (1 + 0.8k) / (1 - k)
ICRLL Approximation
Used to simulate limited Table M by adjusting column used from regular Table M
Occurrence limit reduces variance of aggregate loss distribution, reflecting a similar larger sized risk
Future of ICRLL
No longer needed after NCCI publishes Limited Table Ms
Differences between Table L and Table M
Table L also includes charge for per occurrence limit in addition to charge for aggregate limit
Entry ratios for Table L
r = limited loss / expected unlimited loss
Table L balance equations
Same as Table M, except using Table L charges
Table L, graphically
