Alternative Techniques and Uses of Classification

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Alternative Techniques and Uses of Classification

• Roosevelt C. Mosley, Jr., FCAS MAAA
• Charles A. Bryan, FCAS, MAAA
• CAS Ratemaking Seminar 2002

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Discussion Topics

• Classifications Methods
• New and alternative applications of
  classification methods
• Examples of applications of classification methods

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Principles of Sound Risk Classification System

• Reflect cost and experience differences on the
  basis of relevant risk characteristics
• Applied objectively and consistently
• Practical, cost-effective, and responsive to
  change
• Minimize anti-selection

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Reflect cost and experience differences based on
relevant risk characteristics

• How do we determine which risk characteristics
  are important?
• How do we reflect the cost and experience
  differences between these risks?

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Historically speaking

• Relevant risk characteristics
• Historical experience
• Intuition
• Reflecting cost differences
• One way analysis (loss ratio, pure premium)
• Multi-way tables
• Mini multi-variate analysis

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Where we are today (for the most part)

• Relevant risk characteristics
• Historical experience
• Intuition
• Reflecting cost differences
• One way analysis (loss ratio, pure premium)
• Multi-way tables
• Mini multi-variate analysis

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Some companies are using new techniques

• Generalized Linear Models (GLMs)
• Chi-square Automatic Interaction Detector (CHAID)
• Classification and Regression Trees (CART)

All are multivariate techniques!
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Why use multivariate analysis?

• Traditional Actuarial ApproachAnalyze each
  rating factor independent of all the other
  factors (one way analysis)
• Inherent Assumption Mix of business underlying
  the levels of each factor are the same
• Result Double counting of factor impacts
• Multivariate AnalysisAnalyze each factor
  simultaneously, thus removing the distributional
  bias

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One Way Analysis
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Multi-variate analysis
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Multivariate analysis
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Simple Regression

• y a bx error

Response Variable
Explanatory Variable
y a bx cz dw error
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GLM

• y h(X?) error
• Exponential family of distributions
• Normal
• Poisson
• Gamma
• Binomial

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Examples

• Frequency Model
• y exp(X?) error, y Poisson
• Severity Model
• y exp(X?) error, y Gamma
• Retention Model
• y 1 / (1 exp(- X?)) error, y Binomial

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Generalised Linear Models

• LINEAR MODELS GLM
• µ X? µ h(X?)
• Inverse of
  h, g, is called the
• link function
• Variance independent Variance function
• of the mean of the mean
• Randomness is Normal Randomness is
  Exponential Family (Normal, Poisson,
  Gamma, Binomial)

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CHAID Analysis

• Process used to analyze a dependednt variable
• Subdivides population of risks based on subsets
  of independent variable characteristics
• Goal partition data into mutually exclusive,
  exhaustive subsets
• Does not address rate relativities associated
  with the final categories

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CHAID Analysis An Example
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Examples of Uses of Classification Techniques

• Roosevelt C. Mosley, FCAS, MAAA
• MHL / Paratus
• 2002 CAS Ratemaking Seminar

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Examples of Applications

• Pricing application of renewal modeling
• Flexible multi-factor underwriting model

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Renewal Modeling

• Background
• Regional non-standard insurer
• Significant indicated rate need
• Historical retention in the mid 60s
• Question
• If we take the indicated rate need, what will
  that do to the ability to retain business?

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Approach

• GLM analysis of frequency and severity
• Included factors currently rated on
• Renewal analysis
• Included factors from GLM analysis, plus
• Competitive index
• Renewal premium

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Class Renewal Likelihood
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Competitive Position
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Demand for Renewal
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Renewal Impact on Projected Loss Ratios
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Application Flexible Underwriting Plan
One Strike and Youre Out Approach
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More Equitable Approach
0-1 Not at Faults
2 Not at Faults
Etc...
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More Flexible, Equitable Approach
Factor 1
Factor 2
Factor N

The more factors you include, the more important
a multi- variate analysis becomes!
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Conclusion

• Many other applications are possible
• New approaches have implications for areas other
  than pricing and underwriting
• Maximizing the benefit of the enormous
  information available