Siewart

Question 1

loss ratio approach: advantages

Answer 1

• Can be used when no data available or when data is immature
• LR estimates can be consistently tied to pricing programs
• Relies on more credible pool of company and industry experience

Question 2

loss ratio approach: disadvantages

Answer 2

• Ignores actual emerging experience (not as useful for mature years)
• Industry data may not be applicable to the company’s book of BoB

Question 3

per occurrence excess loss

Answer 3

P*E*x

Premium*ELR*per occurrence charge/excess ratio

Question 4

per aggregate excess loss

Answer 4

P*E*(1-x)*phi

phi is per aggregate charge/aggregate ratio

Question 5

ultimate excess loss formula

Answer 5

P*E*x+P*E*(1-x)*phi

Question 6

implied development approach process

Answer 6

• Develop full coverage losses to ultimate
• Determine ultimate excess losses = ult full coverage – ult limited

Question 7

implied development approach: advantages

Answer 7

• Provides estimate of excess loss at early maturities even when excess loss have not emerged
• estimates the ultimate excess losses using more stable development patterns from the limited loss triangle
• Estimating deductible loss help determine asset value represented by service revenue

*limited losses develop faster and is more stable than excess

Question 8

implied development approach: disadvantage

Answer 8

-Does not explicitly recognize excess loss development

Question 9

why is it appropriate to index deductible for inflation

Answer 9

because it keeps the proportion of deductible/excess losses constant about the limit from year to year

Question 10

direct development approach

Answer 10

Focus on excess development directly

Question 11

direct development approach: advantage

Answer 11

-Explicitly recognizes excess loss development

Question 12

direct development approach: disadvantages

Answer 12

• Excess factors tend to be overly leveraged and extremely volatile
• If excess losses have not yet emerged, cannot estimate IBNR

Question 13

formulas for development factors for LDF^L and XSLDF^L

Answer 13

LDF^L = LDF*R^L/R_t^L

XSLDF^L=LDF*(1-R^L)/(1-R_t^L)

R: severity relativity (limited severity/unlimited severity), ratio of reported losses

R should decrease with time

these formulas can be used for CDFs and LDFs, the formula above is for CDF but can adjust to make LDF by adjusting R^L

Question 14

unlimited LDF formula aka credibility formula

Answer 14

LDF=R_t^L*LDF^L+(1-R_t^L)*XSLDF^L

weighted average of excess and limited LDFs

Question 15

Credibility weighting/BF

Answer 15

-Relies on weighting indications based upon actual experience (direct development) with expected values (loss ratio approach)

U=Z*O*LDF + (1-Z)*E

O: observed loss at time t, LDF: age to ultimate, E: expected ult loss

*If set Z=1/LDF, end up with BF estimate for ultimate loss

U=O + E*(LDF-1)/LDF

*E is expected excess loss and LDF is XSLDF

Question 16

credibility weighting: advantages

Answer 16

• Can determine liabilities either directly or indirectly
• Gives us ability to tie into pricing estimates for recent years where excess losses have yet to emerge
• Provides more stable estimates over time

Question 17

credibility weighting: disadvantage

Answer 17

-Ignores actual experience to extent of complement of credibility, may need to find weights that are more responsive to actual experience

Question 18

service revenue and calculation

Answer 18

-Revenue associated with servicing claims under high deductible program - needs to be reflected on asset side of balance sheet

service revenue = LM*(Ult limited losses - ult excess of aggregate limit)

service revenue asset = service revenue - collected service revenue