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

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Dealing with Model Uncertainty – Primary Writers

CAS Annual Meeting

Stuart Mathewson

GE ERC - Commercial Ins.

November 10, 2003

issues
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?
options
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
options1
Options

Option 1

  • Single model
single model
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?
single model1
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 PML:Premium ratio
      • Incremental excess AAL
single model2
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
options2
Options

Option 2

  • Multiple Models
multiple models
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
multiple models1
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
multiple models2
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
multiple models3
Multiple Models
  • Portfolio Analysis Example
    • Run two models
      • Combine pertinent statistics
        • Weighted average, by region and peril
        • Straight average unless good knowledge
conclusions
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