Mack (1994)

Question 1

Describe two problems with using the normal distribution as an approximation for the true distribution of R, and identify an alternative to the normal distribution

Answer 1

-If the data is skewed, it is a poor approximation -The confidence interval can have negative lower limits, even if a negative reserve is not possible -Lognormal distribution

Question 2

Provide 3 different variance assumptions for Cik

Answer 2

-Proportional to 1 -Proportional to Cik -Proportional to Cik^2

Question 3

The standard error formula does not provide an estimate for a(I-1)^2. Provide 3 options for a(I-1)^2

Answer 3

-Set equal to 0 -Extrapolate the series using log linear regression -Set equal to min(a(I-2)^4/a(I-3)^2, min(a(I-2)^2,a(I-3)^2

Question 4

List the 3 Assumptions of the Chainladder method: Using Formulas

Answer 4

Question 5

List the 3 Assumptions of the Chainladder method: Using Words

Answer 5

1. Expected Incremental Losses are proportional to Losses Reported to Date 2. Losses in each Accident Year are independent of losses in other Accident Years 3. Variance of incremental losses is proportional to losses reported to date

Question 6

Answer 6

Question 7

Confidence interval of reserves-normal distribution

Answer 7

Question 8

Confidence interval of reserves-Lognormal distribution

Answer 8

Question 9

When graphing residuals-what are we looking for and what are we testing?

Answer 9

Question 10

For the calendar year test, what is the mean and variance of Zn?

Answer 10

Question 11

Test for correlation of adjacent development factors

Answer 11

Question 12

Formula for residuals

Answer 12

Question 13

Answer 13

Question 14

The first implicit assumption underlying the chain-ladder method states that information contained in Ci,I+1 i cannot be augmented by using other Cik. Describe a major consequence of this assumption. In addition, briefly describe a procedure for testing this assumption.

Answer 14

• A major consequence is the assumption that development factors are uncorrelated
• To test this, we can run a statistical test where the test statistic is Spearman’s rank correlation. If our test statistic lies within a specified confidence interval around the true correlation, we fail to reject the null hypothesis that development factors are uncorrelated

Question 15

The second implicit assumption underlying the chain-ladder method states that accident years are independent. Describe a major consequence of this assumption. In addition, briefly describe a procedure for testing this assumption. The second implicit assumption underlying the chain-ladder method states that accident years are independent. Describe a major consequence of this assumption. In addition, briefly describe a procedure for testing this assumption.

Answer 15

• A major consequence is the assumption that CY effects do not exist
• To test this, we can run a statistical test to determine if diagonals exist where “small” development factors are prevalent (i.e. the development factors along the diagonal are smaller than usual). If our test statistic lies within a specified confidence interval around the true correlation, we fail to reject the null hypothesis that accident years are independent

Question 16

Provide three options for alpha (I-3)

Answer 16

Question 17

Briefly describe two problems with using the normal distribution as an approximation to the
true distribution of R.

Answer 17

⇧ If data is skewed, it is a poor approximation
⇧ The confidence interval can have negative lower limits, even if a negative reserve is not possible