LEARNING OUTCOMES

　　The candidate is expected to be familiar with survival, severity, frequency and aggregate models, and use statistical methods to estimate parameters of such models given sample data.  The candidate is further expected to identify steps in the modeling process, understand the underlying assumptions implicit in each family of models, recognize which assumptions are applicable in a given business application, and appropriately adjust the models for impact of insurance coverage modifications.

　　Specifically, the candidate is expected to be able to perform the tasks listed below:

　　LEARNING OUTCOMES

　　A. Severity Models

　　1. Calculate the basic distributional quantities:
　　a) Moments,
　　b) Percentiles,
　　c) Generating functions.
　　2. Describe how changes in parameters affect the distribution.
　　3. Recognize classes of distributions and their relationships.
　　4. Apply the following techniques for creating new families of distributions:
　　a) Multiplication by a constant,
　　b) Raising to a power
　　c) Exponentiation,
　　d) Mixing.
　　5. Identify the applications in which each distribution is used and reasons why.
　　6. Apply the distribution to an application, given the parameters.
　　7. Calculate various measures of tail weight and interpret the results to compare the tail weights.
　　8. Explain the properties of the lognormal distribution.
　　9. Explain the Black-Scholes formula as a limited expected value for a lognormal distribution.

　　B. Frequency Models

　　a. For the Poisson, Mixed Poisson, Binomial, Negative Binomial, Geometric distribution and mixtures thereof (as well as compound distributions):
　　1. Describe how changes in parameters affect the distribution,
　　2. Calculate moments,
　　3. Identify the applications for which each distribution is used and reasons why,
　　4. Apply the distribution to an application given the parameters.

　　C. Aggregate Models

　　1. Compute relevant parameters and statistics for collective risk models.
　　2. Evaluate compound models for aggregate claims.
　　3. Compute aggregate claims distributions.

　　D. For severity, frequency and aggregate models

　　1. Evaluate the impacts of coverage modifications:
　　a) Deductibles,
　　b) Limits, and
　　c) Coinsurance.
　　2. Calculate Loss Elimination Ratios.
　　3. Evaluate effects of inflation on losses.

　　E. Risk Measures

　　1. Calculate risk measures VaR, CTE and explain their use and limitations

　　F. Ruin Theory

　　1. Calculate survival and ruin probabilities using discrete models.
　　2. Describe the considerations included in a ruin model

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