Multivariate Risk Classification¶
Minimum Biases Procedures, GLM Basics, Diagnostics, Data Mining Techniques.
Benefits of Using Multivariate Risk Classification¶
- Focus on signal (not noise).
- Provide statistical Diagnostics.
- Consider for exposure correlation.
- Exposure correlation: 75% of 16-year-old drivers are male, but 50% of 50-year-old drivers are male. With age, we can infer something about the sex of the driver.
- Consider for response correlation.
- Response correlation: 16-year-old males have twice the claim frequency as 16-year-old females, if frequency is our response/target.
Minimum Bias Procedures¶
Assume there are two variables: Class and Territory.
Steps¶
- Set up equations. Assume the class relativities to be variables (\(c_{A}, c_{B}, c_{C}\)) and territory relativities to be (\(t_{1},t_{2},t_{3}\)).
- Start with seed relativities for (\(c_{A}, c_{B}, c_{C}\)) and solve for (\(t_{1},t_{2},t_{3}\)).
- Then plug in the t-relativities to solve for c-relativities.
- Iterate until convergence.
- Rebase them.
Advantages¶
- Properly corrects exposure correlation.
Disadvantages¶
- Doesn't provide a way to test if the variable is statistically significant.
- Computationally inefficient (iterative method).
Sequential Analysis¶
The only method allowed for California Personal Auto.
Steps¶
- Perform Univariate analysis to obtain single relativities for a single variable.
- Use the Adjusted Pure Premium Approach to indicate relativities for a second variable.
- Do the same for the others, having adjusted for the exposures of the previous variable at each step.
Advantages¶
- Deals with exposure correlation.
Disadvantages¶
- Doesn't have a closed-form solution.
- The solution varies with the order of the variables chosen for the analysis.