Exam (elaborations)
CAS Exam 8_ Section A Assessment With Answer Key 2024/2025
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- University Of Illinois - Urbana-Champaign
CAS Exam 8_ Section A Assessment With Answer Key 2024/2025
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CAS Exam 8_ Section A Assessment WithAnswer Key 2024/2025
Considerations for Which Risk Characteristics to Use (what rating variables to use)
1. Relationship of Risk Characteristics and Expected Outcome
2. Causality
3. Objectivity
4. Practicality (Initial/Ongoing Cost)
5. Applicable Law
6. Industry Practices
7. Business Practices
Considerations in Establishing Risk Classes (what levels of variables to use)
1. Intended Use (ratemaking v reserving)
2. Actuarial Considerations (Homogeneity, Credibility, Practicality)
3. Other Considerations (Law, industry, business)
4. Reasonability of Results
Rates are equitable if
They reflect expected cost differences
GLM Components
Systematic Component and Random Component
Family of Distributions assumed by the Random Component in a GLM
Exponential with E(yi) = μi ; Var(yi) = φ * V(μi) / ωi
where φ = dispersion parameter
ωi = weights
V(μi) = variance function
Dispersion parameter
A constant used to scale the variance in a GLM
Normal Distribution Variance Function
1
,Poisson Distribution Variance Function
μ
Gamma distribution variance function
(μ)^2
Inverse Gaussian Variance Function
(μ)^3
Negative binomial Variance distribution
(μ)*(1+k(μ))
where k is a dispersion parameter allowing the variance to exceed the mean
Binomial distribution variance function
(μ)*(1-μ)
Tweedie Distribution Variance Function
(μ)^p
Logit link function
Ln(μ/(1-μ))
Log link
Ln(μ)
More skewed: inverse Gaussian or gamma
Inverse Gaussian
Distributions used to model claim severity
Gamma/inverse gaussian
Distributions used to model claim frequency
Poisson, over dispersed poisson, negative binomial distribution
Overdispersed poisson
Allows phi to not be equal to 1 so var (y) can be > mu (Var(y) = phi * mu)
Negative binomial distribution
, Poisson distribution where lambda is a gamma distribution
Distributions used to model pure premium
Tweedie distribution (point mass at 0, right skewed) with p between 1.5 and 1.8
What special case of tweedie becomes a Poisson distribution?
P=1
What special case of tweedie becomes a gamma distribution ?
P=2
How to determine p when fitting a tweedie distribution to a pure premium model?
1. Use model fitting software
2. Test different options and see which optimizes a particular metric
3. Judgmentally choose
Tweedie mean, variance, p, dispersion parameter, relationship to gamma distribution
μ = λ * (αΘ)
Var = φμ^p
P = (α+2)/(α+1)
CV (gamma dist) = 1/sqrt(α)
φ = (λ^(1-p)*(αΘ)^(2-p))/(2-p)
Tweedie distribution assumption that may not be realistic in practice
frequency and severity move in the same direction
Binomial distribution link function
Logit link
Odds
Odds = μ/(1-μ)
Uses for an offset term in a GLM
1. Incorporate pre determined values for certain variables (ex: deductible variable measured in separate
model)
2. When target variable varies directly by a particular variable (claim count/exposure)
if using a logit link: the interpretation of coefificients is that each unit increase in a given predictor
variable increases the odds by
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