Dealing with Model Uncertainty

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Dealing with Model Uncertainty Primary
Writers CAS Annual Meeting Stuart Mathewson GE
ERC - Commercial Ins.
November 10, 2003
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Issues

• Primary writers are using cat models to monitor
  portfolio accumulations and profitability, to
  make reinsurance buying decisions and to price
  the catastrophe perils.
• Reinsurance companies use the modeling data to
  price and underwrite primary company cat
  protection
• As we have seen, single models have built-in
  uncertainties and biases
• How can we feel more comfortable with the cat
  decisions we make, as they are based on model
  output?

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Options

• Single model
• Challenge is to deal with bias and uncertainty
• Multiple models
• Should reduce bias and uncertainty
• Challenge is to deal with different, often
  diverse, results

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Options

• Option 1
• Single model

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Single Model

• Pros
• Resources and model costs are less with one model
• Easier to get to understand one model
• Cons
• One model may bias your portfolio
• To truly reflect uncertainty, may require high
  load ? uncompetitive?
• How do we determine an appropriate loading?

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Single Model

• Pricing Risk Load Options
• Assume pricing starts with Expected Loss (AAL)
• Risk Loads can be based on Account uncertainty
  (stand-alone)
• E.g., a percent of Standard Deviation
• Or -- Risk Loads can be based on incremental
  effect on portfolio uncertainty
• E.g., change in portfolio standard deviation
• Or Risk Loads can incorporate changes in key
  portfolio measures
• Change in PML or PMLPremium ratio
• Incremental excess AAL

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Single Model

• Portfolio Analysis
• The differences between models on a portfolio
  basis are not as great
• One strategy is to manage to higher PML level
• Talk to reinsurers or other modeling experts
  about their opinions of your single model
  vis-a-vis others for the regions and perils in
  the portfolio

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Options

• Option 2
• Multiple Models

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Multiple Models

• Pros
• Biases will often offset one another
• Takes advantage of multiple expertise
• Reinsurance market uses multiple models
• May give more accurate price take advantage of
  others who use only one model
• Cons
• Resources
• More complicated explanations to reinsurers and
  internal underwriters

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Multiple Models

• How do we use the results of various model for
  pricing and portfolio analysis?
• Key parameters
• AAL
• SD
• Various levels on the PML (EP) curve
• Mathematically combining model output, or
• Looking at each model output separately, with
  judgmental decisions based on model knowledge
• Should need less load for parameter uncertainty

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Multiple Models

• Pricing Options
• Run two models
• Combine pertinent statistics
• Weighted average, by region and peril
• Straight average unless good knowledge
• Run one model, after calibration with a second
• I.e., run both in detail for comparisons
• Create pricing adjustments based on region and
  peril comparisons

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Multiple Models

• Portfolio Analysis Example
• Run two models
• Combine pertinent statistics
• Weighted average, by region and peril
• Straight average unless good knowledge

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Conclusions

• Yes, cat models have a significant uncertainty
• But, they are significantly better than old
  rating methods or rules of thumb
• And, there are ways to account for the
  uncertainty in pricing and portfolio analysis
• So, do we trust models? Yes, as long as we
  understand the uncertainties and can account for
  them
• And, the level of trust varies significantly
  based by peril and region