Meyers Flashcards
State 3 reasons why model may not accurately predict distribution of actual outcomes.
- Insurance losses are too dynamic to be fully reflected in a single stochastic model.
- Other models may better fit the data.
- Data used for calibrating the model might be missing key information to make accurate predictions.
Name 2 graphical tests for validity of Mack Model assumptions (uniform distribution of percentiles)
- Histogram: bars of equal height
2.P-P plot: sorted predicted percentiles should follow the expected percentiles along 45 degrees line
expected = 100*i/(n+1)
Briefly explain how to test Model Validity using Kolmogorov-Smirnov Test
Critical value: 136/n^0.5
n = # percentiles
expected = fi = 100*i/n
Di = abs(pi - fi)
D = max(Di)
H0: percentiles are uniformly distributed
If D > critical value, reject H0
If D < critical value, cannot reject H0 (conclude that percentiles are uniformly distributed and Mack Model is appropriate)
How can you recognize a Ligh-Tailed model from histogram and p-p plot
Tallest bars at lowest and highest percentiles in histogram.
P-P plot has an S-shape.
How can you recognize a Heavy-Tailed model from histogram and p-p plot
Tallest bars in the middle of histogram (normal distribution shape)
P-P plot has an inverted S-shape
How can you recognize a Biased high model from histogram and p-p plot
Tallest bar at lowest percentile
P-P plot is bowed down.
How can you recognize a valid model from histogram and p-p plot
P-P plot follows a straight 45 degrees line
Bars in histogram are of equal height.
Is Mack Model for Incurred Loss validated?
No, Incurred Mack model is too light in the tails.
Histogram shows more high/low percentiles than expected
P-P plot shows a slanted S curve and K-S test fails at the 5% level for all lines combined.
Is Mack Model for Paid Loss validated?
No, Paid Mack model is biased high.
Histogram and p-p plot show more low percentiles than expected.
K-S test fails at 5% for all lines combined.
Is Bootstrap ODP Model for Paid Loss validated?
No, ODP Bootstrap model is biased high.
Histogram and p-p plot show more low percentiles than expected.
K-S test fails at the 5% level for all lines combined.
Briefly explain Leveled Chain Ladder (LCL) model and whether it is validated
LCL uses random level parameters for each AY.
uw,d = aw + bd
Loss_w,d follow lognormal distribution (uw,d , sigma_d)
LCL is still too light in the tills but better than Mack.
Histogram and p-p plot show more high/low percentiles than expected.
K-S test fails at 5% for all lines combined.
Briefly explain the Correlated Chain Ladder (CCL) model and whether it is validated
CCL allows for correlation between accident years.
u1,d = a1 + bd
uw,d = aw + bd + rho*(ln(C_w-1,d) - u_w-1,d)
Loss_w,d follow lognormal distribution (uw,d , sigma_d)
Rho is generally positive (result in higher prediction variance than LCL)
CCL is validated, but has mildly thin tails.
Histogram and p-p plot show slightly more high/low percentiles than expected and the K-S PASSES the 5% level.
Briefly explain the Correlated Incremental Trend (CIT) model and whether it is validated
CIT includes a calendar-year trend for incremental paid loss.
CIT allows for correlation between Ays (like CCL)
CIT is biased high on paid losses.
Histogram and p-p plot show more low percentiles than expected.
K-S test fails at the 5% level for all lines combined.
Calculate Inc Loss from CIT model
uw,d = aw + bd + tau(w+d-1)
Zw,d follows lognormal distribution (uw,d , sigma_d)
Inc Loss_1,d follows normal (Z1,d , delta)
Inc Loss_w,d follows normal (Zw,d + rho(IncLoss_w-1,d - Zw-1,d)*e^tau , delta)
LIT is a special case with rho=0.
Briefly explain the Changing Settlement Rates (CSR) model and whether it is validated.
CSR parameter v reflects changes to the claims settlement rate.
uw,d = aw + bd*(1-v)^w-1
Loss_w,d follows lognormal (uw,d , sigma_d)
v is generally positive, reflecting a speedup in payment pattern.
Histogram and p-p plot show that CSR corrects the high bias of other Bayesian paid models and K-S test passes at 5%.
CSR model is validated.
Define Process Risk
Average variance of outcomes from expected result.
Define Parameter Risk
Variance due to uncertainty in the parameters, reflected in the posterior distributions of the parameters.
Represents the overwhelming majority of the total risk in the loss data sets that Meyers looks at.
Define Model Risk
The risk that we did not select the “correct” model.
Meyers does not explore model risk. It could be reflected by weighting together multiple models.
Define Total Risk
Total Risk = Process Risk + Parmeter Risk
Total Risk = EVPV + VHM
Total Risk = E(V(X given theta)) + V(E(X given theta))
Name the 3 models Meyers tested on Incurred Data
- Mack (Light-Tail)
- LCL (Light-Tail)
- CCL (Validated, mildly light tail)
Name the 6 models Meyers tested on Paid Data
- ODP (Biased High)
- Mack (Biased High)
- CCL (Biased High)
- LIT (Biased High)
- CIT (Biased High)
- CSR (Validated)
State 2 reasons that might explain model produces expected loss estimates that are biased high when modelling paid losses.
- Ins Loss environment has experienced changes that are not observable at current time.
- There are other models that can be validated.
Describe 2 ways to increase the variability of the predictive distribution
- Treat level of each AY as random (ex: LCL)
- Allow for more correlation between Ays (ex: CCL)
Which of LCL and CCL produce the highest standard deviation.
CCL since it includes correlation parameter which increases variability.
Is LCL and CCL standard deviation higher or lower than Mack?
Higher since they predict more risk.
2 consequences of inclusion of payment year trend in model
- Model should be based on incremental paid loss amounts rather than cumulative paid loss amounts.
This is because cum loss includes settle claims which do not change with time. - Incremental paid loss amounts tend to be skewed to the right and are occasionally negative.
We need a loss distribution that allows for these features (ex: skew normal)
Compare relationship between sigma_d and d in CIT vs CCL
Since CCL is applied to cum losses, s_d decreases as d increases because greater proportion of claims are settled (less variability).
Since CIT is applied to incremental losses, s_d increases as d increases because smaller, less volatile claims tend to be settled earlier.
Contrast LIT and CIT
LIT is similar to CIT, but it does not include AY correlation.
LIT produce worser results than CIT.
Neither show improvement over ODP or Mack.
True or False?
Meyers conclusions apply to any dataset.
False
Conclusions apply specifically to the dataset studied by Meyers. Other datasets may exhibit different behaviour.
Describe 2 advantages of Correlated Chain Ladder method
- Incorporates correlation between accident years
- Treats the level of each accident year as random, which allows it to predict more risk
Describe 2 advantages of the Bayesian method
- Incorporates expert opinion into the simulation
- Produces full predictive distribution rather than just a point estimate
