Meyers

Question 1

Reasons models may not accurately predict distributions of data (3)

Answer 1

1. insurance process is too dynamic to be captured by a single model
2. other models could better fit data
3. data used to calibrate model was missing crucial information (ex: changes in claims handling, underlying business changes, etc.)

Question 2

Tests for uniformity and descriptions (2)

Answer 2

1. histogram - bars of equal height
2. p-p plot and Kolmogorov-Smirnov (K-S) test - plots predicted percentiles against expected percentiles and looks for a diagonal line along y=x

Question 3

K-S test

Answer 3

compare expected vs. model predicted percentiles and set D = max ( abs. value ( difference ) )

reject the null hypothesis of uniformity if D > critical value

Question 4

Possible test outcomes and interpretations of the histogram and p-p plots (4)

Answer 4

1. uniform - relatively flat histogram and p-p plot tightly distributed around diagonal line
2. light tailed - histogram is higher at endpoints and p-p plot has an “S shape”
3. heavy-tailed - histogram is highest in the center and p-p plot has a “sideways S shape”
4. biased high - histogram has the highest frequency at the lowest percentiles, and decreases as expected loss increases; and p-p plot is the curved below the diagonal (right side of a U)

Question 5

Mack model results on cumulative incurred data

Answer 5

symmetric with light tails

Question 6

Significance of light tails on model results

Answer 6

understates the variability of the predictive distribution

Question 7

Bootstrap ODP model results on incremental paid data

Answer 7

non-symmetric and biased high

Question 8

Significance of being biased high on model results

Answer 8

expected losses will be overstated (b/c actual < expected the majority of the time)

Question 9

Potential explanations for why neither the Mack incurred or bootstrap paid ODP model validated (2)

Answer 9

1. changes in the insurance environment which are not yet observable
2. other models exist which can validate

Question 10

Methods to increase the variability of the predictive distribution (2)

Answer 10

1. treat the level of the AY as random
2. allow for correlation between AYs (vs. independence)

Question 11

Mean of the leveled CL model (LCL) - aka mu(w,d)

Answer 11

level of each AY = mu(w,d) = a_w + b_d

a_w = level of log losses for an AY
exp(b_d) = % of losses paid to date

Question 12

Mean of the correlated CL model (CCL) - aka mu(w,d)

Answer 12

a_w + b_d + p*[ln(C_w-1,d) - mu(w-1,d)]

a_w = log losses in each AY
exp(b_d) = % losses reported
p = correlation coefficient

parenthesis: previous AY cumulative claims - previous AY mean

Question 13

Description of the leveled CL (LCL) and correlated CL (CCL) methods

Answer 13

LCL: includes a parameter for the level of each AY

CCL: LCL + parameter for correlation between AYs

Question 14

Relationship between sigma and development age (d) for cumulative vs. incremental losses along with rationale for each

Answer 14

cumulative: as d increases sigma decreases - fewer open claims in later development periods that are subject to random fluctuations

incremental: as d increases sigma increases - smaller, less volatile claims will be settled first

Question 15

Leveled CL results on cumulative incurred data

Answer 15

improvement over Mack model but still produces light tails

Question 16

Correlated CL results on cumulative incurred data

Answer 16

model validates despite thin tails

Question 17

Mack, ODP bootstrap, and CCL method results on incremental paid losses

Answer 17

all biased high

Question 18

Consequences of using a CY trend (2)

Answer 18

Trend applies to incremental losses so:

1. data tends to be right skewed
2. occasionally has negative values

Question 19

Description of correlated incremental trend (CIT) and leveled incremental trend (LIT) methods

Answer 19

CIT - allows correlation between AYs and includes a CY trend parameter (tau)

LIT - CIT without correlation of AYs

Question 20

Description of the changing settlement rate (CSR) method and loss data used

Answer 20

includes a claim settlement rate parameter

uses cumulative loss data

Question 21

Mean of the CIT model - aka mu(w,d)

Answer 21

level of AY = mu(w,d) = alpha(w) + beta(d) + tau * (w + d - 1)

correlation is applied by using a mixed lognormal-normal distribution

Question 22

Mean of the CSR method - aka mu(w,d)

Answer 22

level of AY = mu(w,d) = a_w + b_d * (1 - gamma) ^ (w-1)

Question 23

CIT and LIT model results

Answer 23

still biased high, no noticeable improvement over Mack or ODP bootstrap methods

Question 24

CSR model results and explanation

Answer 24

model validates and corrects bias in other models

> > recognizes speedup in claim settlement over time because claims are reported and settled faster due to advancements in technology

Question 25

Meyers’ findings on relative size of parameter risk vs. process risk

Answer 25

parameter risk is very close to total risk

i.e. there is minimal process risk