Mack 1994, Venter, Shapland

Question 1

Mack Assumption 1

Answer 1

Expected future losses are proportional to loss-to-date

Implies: Independent LDFs

Question 2

Mack Assumption 2

Answer 2

Independent AYs

Implies: No CY effects

Question 3

Mack Assumption 3

Answer 3

Variance of future losses is a function of age and losses-to-date

Question 4

Mack Method Pro and Con

Answer 4

Pro: Get estimated reserve and standard error

Con: Tells us nothing of shape of loss reserve distribution

Question 5

Mack Tests

Answer 5

Assumption 1
-Cuml. loss of adjacent periods
-Correlation test

Assumption 2
-CY Effects

Assumption 3
-Residual plots

Other
-Reasonability check

Question 6

Venter Implications/Tests

Answer 6

1. Significance
2. Superiority of emergence pattern - SSE
3. Linearity - Raw residual vs Prev. Cuml.
4. Stability - Stability Plots
5. No correlation - Correlation test
6. No high/low diagonals - Diagonal dummy regression

Question 7

Stability Plots

Answer 7

1. Residuals over AY
2. Moving average of LDF
3. Instability of obs. around mean vs instability of mean itself over time

Question 8

GLM Bootstrap Pros

Answer 8

-Fewer parameters
-Can add CY trend
-Can model shapes besides triangle
-Allows us to match model parameters to statistical features in data

Question 9

GLM Bootstrap Cons

Answer 9

-Must fit GLM to every sample triangle
-Not easy to explain

Question 10

Bootstrap: L-Year Weighted Average

Answer 10

GLM: Exclude first few diagonals

ODP: Calc LDFs from L-year and exclude from residuals, but must still sample for them

Question 11

Bootstrap: Missing Values

Answer 11

GLM: Not an issue

ODP: 3 Options
-Estimate using surrounding
-Exclude from LDFs and residual calcs
-Latest diagonal: fit like other projections

Question 12

Bootstrap: Outliers

Answer 12

GLM: Treat like missing

ODP: 2 Options
-Treat like missing
-Exclude from LDFs and residuals but include during projections

Question 13

Bootstrap: Many outliers

Answer 13

GLM: 2 Options
-Choose new parameters
-Change error distribution

ODP: 2 Options
-L-year weighted average
-Leave in, might indicate highly skewed residuals

Question 14

Bootstrap: Heteroscedasticity Options

Answer 14

Stratified Sampling
Variance Parameters
Scale Parameters

Question 15

Bootstrap: Partial First Dev

Answer 15

Not issue until projections
Divide latest AY sample reserves by partial year amount (half for six month)

Question 16

Bootstrap: Partial last CY

Answer 16

Annualize losses while parameterizing
Adjust sample triangle back to partial date
Interpolate LDFs to project

Question 17

Bootstrap Tests

Answer 17

Residual Graphs (iid residuals)
Normality
Outliers
Parsimony (implied dev patterns)

Question 18

Bootstrap Reasonability Review

Answer 18

Standard error should increase
CoV should decrease
Totals should be largest/smallest

Question 19

Combining Models Options

Answer 19

Same RVs and weight together
Independent RVs and select one

Question 20

Bootstrap: Aggregating by Business Unit even with Correlation

Answer 20

Location mapping - use same residual positions
Re-sorting - shuffle residuals so they have specified correlation

Question 21

Bootstrap: Fitting a Distribution afterwards

Answer 21

Smooths results
Prevents some random noise from distorting calculations/metrics

Used for:
-Assessing quality of fit
-Estimate extreme values and TVaR

Question 22

Mack Variance Option: Constant Variance

Answer 22

LDF: sumproduct(age1,age2) / sumproduct(age1,age1)

Residual: A-E

Question 23

Mack Variance Option: Variance Prop. to C

Answer 23

LDF: Weighted average

Residual: (A-E)/sqrt(Prev)

Question 24

Mack Variance Option: Variance Proportional to C^2

Answer 24

LDF: Simple average of LDFs

Residual: (A-E)/Prev