Dealing with Model Uncertainty – Primary Writers CAS Annual Meeting Stuart Mathewson GE ERC - Commercial Ins.

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

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 • 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

Options Option 1 • 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 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 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

Options Option 2 • 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 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 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 Models • Portfolio Analysis Example • Run two models • Combine pertinent statistics • Weighted average, by region and peril • Straight average unless good knowledge

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

Dealing with Model Uncertainty – Primary Writers CAS Annual Meeting Stuart Mathewson GE ERC - Commercial Ins.