What are the pros and cons of univariate approaches?
- They do not take into consideration other variables
- They are distorted by distributionnal bias and the results can also be heavily distorted by unsystematic effects (noise).
- The result is a set of answers with no additional information about the certainty of the results.
- Interactions can be incorporeted but only with two-way or three-way analysis
What is the primary advantages of univariate approaches?
Easy to understand and transparency results.
What are the pros and cons of the mimimum bias methods?
Pros
- Account for eneven mix of business
- High transparency
Cons
- Computationally inefficient
- No diagnostics are included
What are the pros and cons of the multivariate methods?
Pros:
- Consider all rating variable -> adjust for exposure correlation
- Remove noise and capture signal
- Produce model diagnostics
- Allow interaction
cons:
- Lack of transparency (glm can still be good)
Why the balancing of the fundamental insurance equation is necessary at a individual level?
Because otherwise, the compagnies would subject to adverse selection, resulting in financial deterioration.
Explain adverse selection.
Adverse selection is the process that happen when a compagny have bad segmentation, resulting in all low-risk leaving and high-risk coming.
What a compagny can do to break the adverse selection circule?
- Improve segmentation
- Become insolvant
- Specialise in high risk only and raise rate accordingly
Balancing the insurance equation at the aggregate level brings __?
Balancing the insurance equation at the individual level brings __?
Aggregate = profitability
Individual = competivity
What is the favorable selection? What are the two option that a compagny can do when they are in a favorable selection possition?
It when a compagny identify a new rating variables that other don’t have, given a competitif advantage.
- Implement the new variable in rating -> better segmentation -> better low-risks
- Risk Selection -> better risk will increase profitability -> long-term rate will decrease.
What are the 4 criteria for evaluating rating variables?
- Statistical
- Operational
- Social
- Legal
In variable selection, explain what is the statistical criteria?
The rating variables should reflect the variation in expected costs among different groups of insureds.
- Statistical signifiance
- Homogeneity -> group of similar risk
- Credibility -> group large enough and/or stable enough
In variable selection, explain what is the operational criteria?
The variable should be practical to use:
- Objective -> objective definition
- Inexpensive to administer
- Verifiable -> should not be manipulate by the inssured
Complete; The goal of classification is to balance ___
Grouping into sufficient level to be homogeneous while having stability (credibility) in these groups.
In variable selection, explain what is the Social criteria?
Insurance cie are affected by social perception
- Affordability
- Causality -> direct impact to the amount of expected loss
- Controllability -> the inssured have some control to his class
- Private concerns
In variable selection, explain what is the Legal criteria?
Each state/province have law and regularisation to be sure that rate are “not excessive, not inanequate, and not unfairly discriminatory”.
What is self-selection?
Self-selection is when a product is on volunter base, only the risk that have advantage to take it will take it -> biased data.
What are the distortion of the Pure Premium Approach in Risk Classification.
- The method assume a uniform distribution of exposure across all other rating variable (assume no exposure correlation).
- Can create a double count effect if exposure are correlated
- Can be hard to allocate ULAE to the differents class, so the pure premium used may only include ALAE.
What are the distortion of the Loss Ratio Approach in Risk Classification.
- Can be hard to allocate ULAE to the differents class, so the pure premium used may only include ALAE.
- Adjuste for distributional bias but will yield true relativities only if other variables relativities reflect the true value.
- The method will adjust for inequity present in other variable.
What are the distortion of the adjusted pure premium Approach in Risk Classification.
Same results as with the Loss Ratio method.
- Can be hard to allocate ULAE to the differents class, so the pure premium used may only include ALAE.
- Adjuste for distributional bias but will yield true relativities only if other variables relativities reflect the true value.
- The method will adjust for inequity present in other variable.
Why the multivariate method were adopted?
- Computer power increased -> data no longuer need to be aggregated
- More granularity and accessibility of the data
- Competitive pressure -> Not to be in adverse selection
What are the different type of Minimum Bias Procedure.
- Rating structure
- Additive
- Multiplicative
- Combined
- Bias function
- Balance principle
- Least square
- Chi-deux
- Miximum likelihood
What is the Sequential Analysis.
It is a Minimum Bias Procedure with one iteration. The order of variable will affect the results.
Why GLMs are the most used multivariate method?
- Each iteration can be analysed
- Easy to understand
- Produce a serie of multiplier - which is what the insustry is used.
What is the difference between the GLM and LM models?
The GLM remove the normality and constant variance assumption.
