Aggregate Excess Loss Cost Estimation

Question 1

Advantage of using vertical slices

Answer 1

Size method

More intuitive

Question 2

Advantage of using horizontal slices

Answer 2

Layer method

Faster if calculating XS losses for multiple limits

Question 3

Entry ratio

Answer 3

Ratio of actual loss to expected loss

Used to adjust for size of risk

Question 4

Table M charge, definition

Answer 4

Expected percent of losses > rE

Question 5

Table M savings, definition

Answer 5

Expected percent of losses < rE

Question 6

Table M process

Answer 6

Find all given r

Ø(r_i) = (r_i+1 - r_i) * % of risks above r

Ø(r_max) = 0

Savings = Ø + r - 1

Question 7

Why Table M charge columns would be needed for different risk sizes

Answer 7

Variance of aggregate loss distribution will vary by risk size

Larger size, less variance

Question 8

Diagram representing Table M charge and savings

Answer 8

Question 9

Formulas for Table M charge and savings, continuous distribution

Answer 9

Question 10

First and second derivatives of Table M charge and savings

Answer 10

Question 11

What happens to charge and savings as entry ratio and risk size go to infinity

Answer 11

Variance in ratios goes to zero, so curve will flatten

Charge becomes max (0, 1 - r)

Question 12

How an error in estimation of expected losses impacts insurance charge

Answer 12

% error is greatest for large policies with high r

$ error is greatest for large policies with low r

Question 13

Adjusted expected losses for a risk

Answer 13

Expected losses x State Hazard Group Differential

Question 14

Purpose of State Hazard Group Differential

Answer 14

Some policies of same size are riskier than others

Differential adjusts expected losses to match those of a different size but same distribution shape

Question 15

How NCCI moving to expected claim counts (instead of losses) will change risk mapping

Answer 15

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

Question 16

Guaranteed Cost Premium

Answer 16

GCP = (e + E[A])T

Question 17

Expected retrospective premium

Answer 17

E[R] = (B + c(E[A] - I))T

Question 18

Basic Premium formula

Answer 18

B = e - (c - 1)E[A] + cI

Question 19

Expense component of basic premium

Answer 19

e - (c - 1)E[A]

Question 20

Value, or charge difference

Answer 20

Only true if the plan is balanced

Question 21

Entry difference

Answer 21

Always true

Question 22

Limited Table M entry ratios

Answer 22

r* = limited losses / expected limited losses

Question 23

Basic premium with limited Table M

Answer 23

B^LM = e - (c - 1)E[A] + c(I^LM + kE[A])

k = 1 - expected limited losses / expected unlimited losses

Question 24

Excess Loss Pure Premium Factor (also called excess ratio)

Answer 24

k = 1 - expected limited losses / expected unlimited losses

Question 25

Balance equations, limited Table M

Answer 25

Same as Table M balance equations but with expected limited loss on the denominator

Question 26

Relationship between expected losses and insurance charge

Answer 26

E[L] = E[A] - I

Question 27

ICRLL definition

Answer 27

Insurance Charge Reflecting Loss Limitation

Question 28

ICRLL approximation, adjusted expected losses

Answer 28

Adjusted Expected Loss = E[A] x SHG differential x (1 + 0.8k) / (1 - k)

Question 29

ICRLL Approximation

Answer 29

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

Question 30

Future of ICRLL

Answer 30

No longer needed after NCCI publishes Limited Table Ms

Question 31

Differences between Table L and Table M

Answer 31

Table L also includes charge for per occurrence limit in addition to charge for aggregate limit

Question 32

Entry ratios for Table L

Answer 32

r = limited loss / expected unlimited loss

Question 33

Table L balance equations

Answer 33

Same as Table M, except using Table L charges

Question 34

Table L, graphically

Answer 34