Mack (1994)

Question 1

3 Assumptions of CL method

Answer 1

1. Expected incremental losses are proportional to losses reported to date
2. Losses in each AY are independent
3. Variance of incremental losses is proportional to losses reported to date

Question 2

Selected LDF for variance assumption alpha squared times c^2

Answer 2

Simple average

Question 3

Selected LDF for variance assumption alpha squared * c

Answer 3

Weighted average

Question 4

Selected LDF for variance assumption alpha squared * 1

Answer 4

Least Squares

Question 5

Confidence interval of reserves, normal

Answer 5

R +/- Z * standard error

Question 6

Confidence interval of reserves, lognormal

Answer 6

mu = Re^[-sigma^2/2 + Z*sigma]
sigma^2 = ln[1 + (se/R)^2]

Question 7

Graphing residuals (Mack 1994)

Answer 7

Testing assumption 3 – looking for residuals randomly around zero, no downward or upward trend

Question 8

Calendar year test, mean and variance for n = 1 to 6

Answer 8

1: 0, 0
2: 0.5, 0.25
3: 0.75, 0.188
4: 1.25, 0.438
5: 1.563, 0.370
6: 2.062, 0.62

Question 9

Test for correlation of adjacent development factors

Answer 9

1) Tk = 1 - 6S/[n(n^2 - 1)]
n = # rank-pairs in column
2) Weight Tk(s) by n - 1
3) E[T] = 0
4) Var[T] = 2/(N-1)(N-2)

Question 10

Formula for residuals

Answer 10

r = (A - E)/sqrt(E)

Question 11

Graphing c(i,k+1) vs c(i,k)

Answer 11

Testing assumption 1: Linearity of factor