# Actuarial Modeling

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This course prepares students to apply actuarial models for the solving of business problems. Models of survival, frequency, severity and aggregate losses are covered. Students learn how to formulate these models, fit parameters from data, and determine measures of confidence for decisions based upon these models. Students also learn methods based upon Bayesian analysis to adjust models for credibility. Simulation methods are used to obtain estimates from the models covered in this course.

This undergraduate-level course is 7 weeks To enroll, speak with an Enrollment Representative.

#### Course details:

Credits: 4
Continuing education units: XX
Professional development units: XX
Duration: 7 weeks

#### 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.
Tuition for individual courses varies. For more information, please call or chat live with an Enrollment Representative.