act490 | undergraduate
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Bayesian and Cedibility Concepts
- Create credibility adjusted rate estimates using the BÅ«hlmann and BÅ«hlmann-Straub methods for computing credibility factors that approximate Bayesian estimates.
- Apply credibility methods to actuarial ratemaking problems.
- Explain the Bayesian framework for using new data to update previous estimates.
- Create credibility adjusted rate estimates using the limited fluctuation method.
Actuarial Model Characteristics
- Explain basic properties of random variables and probability models.
- Explain terminology used to describe insurance problems.
- Explain moments of probability distributions.
- Measure the tail behavior of probability distributions.
- Select the appropriate probability models for general insurance problems.
- Select the appropriate probability models for life insurance problems.
Claim Severity Models
- Explain the properties of the continuous probability distributions that are frequently used to model insurance claims: uniform, exponential, gamma, Pareto and lognormal.
- Model deductibles and policy limits as modifications to claim distributions.
- Describe the concepts of truncation and censoring of distributions.
- Explain the concepts of finite and continuous mixing of distributions.
- Apply claim model concepts to solve actuarial problems involving insurance coverage and coverage modifications.
Claim Frequency Models
- Explain the properties of the discrete probability distributions that are frequently used to model insurance claims counts: Poisson, binomial and negative binomial.
- Apply the Probability Generating Function (pgf) and the Moment Generating Function (mgf) to claim frequency distributions.
- Explain the recursive definition of the (a, b) class of distributions.
- Apply claim count model concepts to solve actuarial problems.
Aggregate Loss Models
- Explain the statistical properties of aggregate loss models that compound a frequency and severity distribution.
- Model the distribution of an aggregate loss using compound distributions.
- Apply aggregate loss model concepts to solve actuarial problems.
Estimating Empirical Loss Models
- Demonstrate how empirical loss data can be summarized into a table in a way that facilitates estimation of a survival model.
- Construct survival models using the Kaplan-Meier and Aalen-Nolan estimators.
- Construct confidence intervals for survival function estimators.
- Apply empirical model concepts to solve actuarial problems.
Estimating Parametric Loss Models
- Create parametric models of loss data using the method of moments, percentile matching and maximum likelihood method.
- Construct confidence intervals for a maximum likelihood estimator using the delta method.
- Apply distribution estimation concepts to solve actuarial problems.
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