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exam 7 > Meyers > Flashcards

Meyers Flashcards

1
Q

what are three explanations for why models do not accurately predict the distribution of outcomes for test data?

(Meyers)

A
  • insurance process is too dynamic to be captured in a single model
  • other models that better fit the data
  • data used to calibrate the model is missing crucial information needed to make a reliable prediction
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2
Q

what are two examples of ‘crucial information’ needed to make a prediction that models might be missing?

(Meyers)

A
  • changes in claim processes

- changes in the way the underlying business is conducted

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3
Q

what is the underlying assumption for all of the models mentioned in the paper?

(Meyers)

A

there have not been any substantial changes in the insurer’s operations

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4
Q

how does Meyers test the Mack model?

Meyers

A
  • selected 200 incurred loss triangles
  • used Mack model to calculate mean & SD
  • fit logN distr. with mean & SD that matched those produced by Mack model
  • converted actual outcome into a percentile of the logN distribution
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5
Q

what fact do the validation tests of the Mack model leverage?

(Meyers)

A

percentiles from each insurer should be uniformly distributed

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6
Q

what should we expect from the histogram test?

Meyers

A

-if percentiles are uniformly distributed, height of the bars should be equal
(not perfectly level with small sample)

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7
Q

what do p-p plot and Kolmogorov-Smirnov tests test for?

Meyers

A

test for statistical significance of uniformity

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8
Q

what do we expect a p-p plot/KS test to look like?

Meyers

A
  • p-p (predicted percentiles) plot expect to be along a 45-degree line
  • K-S creates a ‘boundary’ around that line
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9
Q

when do we reject the hypothesis that a set of percentiles is uniform, under the K-S test?

(Meyers)

A

when K-S statistic is GREATER than its critical value

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10
Q

if the actual outcomes fall into the smaller and large percentiles of the distributions produced by the Mack model more often than the middle percentiles, what can we conclude?

(Meyers)

A

conclude that Mack model produces a distribution that is light-tailed

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11
Q

if the Mack model produces larger tails, what can we expect to see on a histogram test?

(Meyers)

A

-outcomes falling in the largest percentile would shift toward the middle percentiles

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12
Q

what does an “S” shape in a p-p plot mean?

Meyers

A

-model is light tailed because actual outcomes are falling into percentiles that are lower than expected in the left tail, and higher than expected in the right tail

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13
Q

what would a backwards “S” shape in a p-p plot imply?

Meyers

A

-Mack model is heavy-tailed

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14
Q

when testing the bootstrap ODP model and Mack models, how did actual outcomes compare to predicted outcomes?

(Meyers)

A

actual outcomes occurred in the lower percentiles of the model distributions more often

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15
Q

what was the result of testing the bootstrap ODP and Mack models?

(Meyers)

A

-implication that both models produce expected loss estimates that are biased high when modeling paid losses

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16
Q

what is the denominator used to calculate the expected value of percentiles for a p-p plot?

(Meyers)

A

n+1

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17
Q

what is the denominator used to calculate the expected value for a K-S test?

(Meyers)

A

n

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18
Q

what does it mean for models to be biased high?

Meyers

A
  • more of the actual outcomes will fall in lower percentiles because the model distributions are shifted too far to the right
  • if they shifted back to the left -> not so many outcomes falling into the left tails
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19
Q

what does a K-S D statistic greater than the critical value indicate?

(Meyers)

A

-uniformity is not present in the model

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20
Q

what differences were there between model results for paid and incurred losses?

(Meyers)

A

incurred: distr. predicted by Mack model has light tails
paid: distr. predicted by Mack and ODP models tend to produce expected loss estimates that are too high

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21
Q

what are possible reasons for the Mack and ODP bootstrap model testing results?

(Meyers)

A
  • insurance loss environment has experienced changes not yet observable
  • there are other models that can be validated
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22
Q

what causes light tails in Mack’s model for incurred loss data?

(Meyers)

A

Mack model underestimates the variability of the predictive distribution

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23
Q

what are two ways to increase the variability of the predictive distribution?

(Meyers)

A
  • treat the level of the AY as random [Mack model multiplies age-to-age factors by last observed loss -> last observed loss acts are fixed level parameters)
  • allow for correlation between AY (Mack assumes loss amounts for different AY are ind’t)
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24
Q

what improvement does the Leveled Chain Ladder (LCL) model make to the Mack model?

(Meyers)

A

treats the level of the AY as random

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25
Q

how does the Correlated Chain-Ladder Model differ from the LCL model?

(Meyers)

A

allows for correlation between each subsequent mu (AY) parameter

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26
Q

how is the level of each AY defined in the LCL model?

Meyers

A

mu_w,d = alpha_w + beta_d

27
Q

how is the level of each AY defined in the CCL model?

Meyers

A

mu_w,d = alpha_w + beta_d + rho * (log(C_w-1,d) - mu_w-1,d)

28
Q

how do the standard deviations of the LCL and CCL models compare?

(Meyers)

A

-CCL model produced significantly higher SD for each AY than LCL
(correlation parameter increases variability)

29
Q

how do the SD of the LCL and CCL compare to the Mack model?

Meyers

A

generally, both LCL and CCL produce higher SD than Mack

30
Q

how does the LCL model do when tested via histogram and p-p plots (incurred)?

(Meyers)

A
  • improvement over Mack model

- some “S” shape implying that the tails are light

31
Q

how do the plots for the CCL model do on incurred loss data?

Meyers

A

-slight S shape, but all points lie inside K-S bounds -> model validates against the data and exhibits uniformity in the percentiles

32
Q

how did the CCL model validate against paid loss data?

Meyers

A

produced estimates that were biased high

33
Q

what important consequences does the inclusion of a payment year trend (within model estimates for paid data) have?

(Meyers)

A
  • model should be based on incremental paid loss amounts rather than cumulative paid loss amounts [settled claims do not change over time]
  • incremental paid loss amounts tend to be skewed to the right and are occasionally negative - loss distr. must allow these features
34
Q

what is a distribution that is skewed to the right and produces negative values?

(Meyers)

A

skew normal distr

35
Q

what are the parameters of the skew normal distr.?

Meyers

A

mu - location param
omega (w) - scale param
delta - shape param

36
Q

how do different values of delta affect the skew normal distribution?

(Meyers)

A
  • delta = 0: normal distr
  • delta -> 1: more skew
  • delta = 1: truncated normal
37
Q

how does the Correlated Incremental Trend (CIT) model estimate loss?

(Meyers)

A
  • introduces a payment trend, tau

- uses a mixed LogN-N distribution to induce skewness and still allow for negative values

38
Q

what is a notable difference about sigma_d between the CIT and CCL models?

(Meyers)

A
  • for CCL model, sigma_d decreased as d increased (CCL model applied to cumulative losses, greater proportion of claims are settled -> less variability
  • CIT model applied to incremental losses, opposite is true, because smaller & less volatile claims tend to settle earlier
39
Q

what is a notable difference about the correlation imposed on the CIT & CCL models?

(Meyers)

A
  • CCL model: correlation feature applies to the log of the cumulative losses
  • CIT model: correlation feature applies outside of the log because there is a possibility of negative incremental losses
40
Q

how do the prior distributions of the CIT model parameters vary from those of the CCL & LCL models?

(Meyers)

A
  • wide prior distributions for CCL & LCL because little is known about claims environment
  • more restrictive prior distr. for tau and sigma params because unreasonable parameters were produced with wide versions
41
Q

how does the Leveled Incremental Trend model compare to the CIT model?

(Meyers)

A

-does not include AY correlation

42
Q

what do the plots of the CIT and LIT models on paid data reveal?

(Meyers)

A
  • CIT and LIT models produce estimates that are biased high

- no noticeable improvement over the ODP or Mack models

43
Q

what was the CSR model built to reflect?

Meyers

A

-reflect speedup in claim settlement

“Changing Settlement Rate” model

44
Q

what type of losses does the CSR model use?

Meyers

A

-cumulative paid losses (vs. incremental)

45
Q

what does a positive value for gamma in the CSR model indicate?

(Meyers)

A

indicates a speedup in claim settlement

causes beta_d * (1-gamma)^(w - 1) to increase with w (AY) -> mean, mu_w,d will increase across w

46
Q

what did the posterior distribution for gamma indicate?

Meyers

A

speedup in claims settlement

47
Q

how did the CSR model perform on paid data, when plotted?

Meyers

A
  • performed well - nearly level histogram, p-p plot close to the y=x line
  • incurred data reviewed earlier recognized the speed-up in claims settlement rate
48
Q

what is the formula (in words) for total risk?

Meyers

A

Total Risk = Process Risk + Parameter Risk

49
Q

what does process risk represent?

Meyers

A

average variance of the outcomes from the expected result

50
Q

what does parameter risk represent?

Meyers

A

variance due to many possible parameters in the posterior distribution of the parameter

51
Q

how does parameter risk for the CCL model compare to total risk, and what does it imply?

(Meyers)

A
  • parameter risk is very close to the total risk

- implies that process risk is minimal

52
Q

what is model risk?

Meyers

A

-risk that we did not select the right model

53
Q

how can we test for model risk?

Meyers

A
  • formulate a model that is a weighted avg of the various candidate models, where the weights are parameters
  • if post. distr. of the weights assigned to each model has significant variability, then model risk exists
54
Q

what portion of total risk does the quantification of model risk show up in?

(Meyers)

A

as process risk

55
Q

overall, what were Meyers’ takeaways from testing on incurred data?

(Meyers)

A
  • Mack model understates variability
  • CCL model allows for correlation among AYs and predicts the distr. of outcomes correctly within a specified confidence interval
56
Q

how did the bootstrap ODP, Mack, and CCL models perform on paid data, and what does it suggest?

(Meyers)

A
  • give estimates of expected ult. loss that are biased high

- suggests there is a change in loss environment not captured in those models

57
Q

how do the CIT and LIT models attempt to improve performance of ODP, Mack, and CCL models on paid data? and do they succeed?

(Meyers)

A
  • introduce payment year trends

- fail to improve

58
Q

how does the CSR model compare to previous models, in both methods and results?

(Meyers)

A
  • introduces parameters to account for speedup in claims settlement rate
  • predicts distr of outcomes correctly within specified confidence interval
59
Q

what is a Markov chain?

Meyers

A

random process where the transition to the next state depends ONLY on its current state, and not on prior states

60
Q

what is the adaptive phase of the Bayesian MCMC model fitting process?

(Meyers)

A
  • user runs a Markov chain through a large number of iterations using a starting vector x_1
  • Markov chain algorithm automatically is modified to increase efficiency
61
Q

what is the burn-in phase of the Bayesian MCMC model fitting process?

(Meyers)

A
  • additional t_2 iterations are run after adaptive phase

- convergence to the limited distr should occur

62
Q

what happens in the final phase of the Bayesian MCMC model fitting process?

(Meyers)

A
  • user runs additional t_3 iterations

- takes a sample from the (t_2+1) step to the (t_2+t_3) step to represent the posterior distr

63
Q

what happens after Markov chains have been run for each param in the model and have converged?

(Meyers)

A

-we sample from these posterior distributions for each parameter a large number of times to create parameter sets for the model

exam 7 (21 decks)

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