Meyer Flashcards
Why the Mack model may not accurately predict the distribution of outcomes for the test data
- The insurance process is too dynamic to be captured in a single model
- There could be other models that better fit the data
- The data used to calibrate the model is missing crucial information needed to make a reliable prediction
Describe when the model is light tailed
For histogram: The actual outcome are falling into the smaller and larger percentiles of the distributions produced by the Mack model more often than the middle percentiles.
For p-p plot, the predicted percentile forms an “S” shape. The actual outcomes are falling into percentiles that are lower than expected in the left tail and higher than expected in the right tail.
This means the model is underestimating variability
Differences between model results for paid and incurred losses for Mack and ODP
Incurred- the distribution predicted by the Mack model has light tails.
Paid - the distributions predicted by the Mack and ODP models tend to produce expected loss estimates that are too high (observation in the graph: actual outcomes are occurring in the lower percentiles of the model distribution more often. More of the actual outcomes will fall in lower percentiles because the model distribution are shifted too far to the right)
Possible reasons: the insurance loss environment has experienced changes that are not yet observable OR that there are other models that can be validated
Two ways to increase the variability of the predictive distribution to solve the issue with underestimating the variability
- The Mack model multiplies the age-to-age factors by the last observed loss. These observed losses act as fixed level parameters. A model that treats the level of the accident years as random will predict more risk.
- The Mack model assumes that the loss amounts for different accident years are independent. A model that allows for correlation between accident years will predict more risk.
Describe the leveled chain ladder (LCL) model
- This addresses the first model improvement
Since this is a Bayesian model, each parameter is given a prior distribution, Since little information is known about the claims environment for these insurers, each parameter is given a wide prior distribution. By giving them wide distribution, the posterior distributions for each parameter will be highly influenced by the data during the Bayesian MCMC process
Describe the Correlated Chain Ladder (CCL) model
Similar to LCL model except it allows for correlation between each subsequent mu parameter
Comparing LCL model and CCL model
CCL model produced significantly higher standard deviations for each AY than the LCL model. (this makes sense because it included the correlation parameter which increased variability)
Both the LCL and CCL model produce higher standard deviation than the Mack Model.
Describe the LCL model on paid and incurred data
Incurred - still showing the ‘S’ shape so the tails are light. But it’s a large improvement over the Mack Model.
Paid - biased high
Describe the CCL model on paid and incurred data
Incurred - may still see an ‘S’ shape, but D statistics is smaller than the critical value. (so this model validates against the data and exhibits uniformity in the percentiles)
Paid -
What’s the consequence of including payment year (CY) trend in the model
- The model should be based on incremental paid loss amounts rather than cumulative paid loss amount. Because cumulative losses include settled 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
Comparing the CIT (Correlated Incremental Trend) model and the CCL model
Since the CCL model was applied to cumulative losses, the standard deviation decreased as age increased since a greater portion of claims are settled (meaning less variability). However, since the CIT model was applied to incremental losses, the standard deviation increased as age increased. Because the smaller less, volatile claims tend to be settled earlier.
In the CCL model, the correlation feature was applied to the log of the cumulative losses. Since there is a possibility of negative incremental losses, the correlation feature was applied outside of the log for CIT.
Describe the Leveled Incremental Trend (LIT) model
Similar to the CIT model but does not include AY correlation
Describe the CIT model and LIT on paid data
Both CIT and LIT models produce estimates that are biased high. (Neither model shows a noticeable improvement over the ODP or Mack models)
Describe the Changing Settlement Rate (CSR) model
using cumulative paid losses without considering a payment year trend
but reflect the speedup in claim settlement
Describe CSR model on paid data
Validated. Performs well on both histogram and p-p- plot
