ACS 4631 - Actuarial Probability Models

4 lecture hours 0 lab hours 4 credits

This course is designed to provide students with a comprehensive understanding of the core mathematical concepts included on the syllabus for the Actuarial Exam in Advanced Short-Term Actuarial Mathematics (Exam ASTAM, offered by the Society of Actuaries). Topics covered include severity models, aggregate models, coverage modifications, construction and selection of parametric models, credibility, reserving and pricing for short-term insurance coverages. Substantial focus will also be placed on developing efficient problem-solving skills. 
Prereq: ACS 3530   
Note: None
This course meets the following Raider Core CLO Requirement: None

• Describe how changes in the parameters affect the distributions
• Create new distributions by multiplication by a constant, raising to a power, exponentiation, mixing and splicing
• Understand and interpret the characteristics of severity distributions
• Compare two distributions based on various characteristics of their tails, including moments, ratios of moments, limiting tail behavior, hazard rate functions, and mean excess functions
• Understand the derivation and characteristics of the Generalized Extreme Value and the Generalized Pareto distributions
• Apply the Generalized Extreme Value and the Generalized Pareto distributions to the estimation of tail risk measures and probabilities. Applications of probabilities using addition and multiplication rules
• Use convolution and recursive formulas to derive probability and distribution functions for aggregate claims distributions with (a,b,0) or (a,b,1) frequency, and with discrete severity distributions
• Derive the discretized version of a continuous distribution using the method of rounding and local moment matching
• Perform calculations for sums of compound Poisson models
• Evaluate the effects of the following coverage modifications: deductibles, policy limits, maximum covered loss, coinsurance, and stop loss reinsurance
• Calculate and interpret loss elimination ratios, increased limits factors, and deductible factors
• Evaluate and interpret the effects of inflation on losses
• Estimate the parameters for frequency and severity distributions by maximum likelihood
• Estimate the variance of the estimators and construct normal and non-normal confidence intervals
• Use the delta method to estimate the variance of the maximum likelihood estimator of a function of the parameter(s)
• Estimate the parameters for severity, frequency, and aggregate distributions using Bayesian Estimation
• Perform model selection using Graphical procedures, Hypothesis tests, (including Kolmogorov-Smirnov, Chi-square goodness-of-fit, and Likelihood ratio (LRT) tests). Score-based approaches, including Schwarz Bayesian Criterion (SBC), Bayesian Information Criterion (BIC), and Akaike Information Criterion (AIC)
• Explain and apply Bayesian (greatest accuracy) credibility
• Apply Bühlmann and Bühlmann-Straub models and understand their relationship to Bayesian models
• Explain and apply empirical Bayesian estimation in the nonparametric and semiparametric cases
• Understand, interpret, and apply techniques for estimating outstanding claims, including Expected Loss Ratio, Chain-Ladder, Bornhuetter-Ferguson, Bayesian, Frequency and Severity

• Understand, interpret, and apply the following statistical models and assumptions used for outstanding claims reserves: 1. Mack’s model, 2. Poisson model 3. Overdispersed Poisson model
• Calculate projected losses using trend analysis
• Calculate overall average rates and rate changes using the loss cost and loss ratio methods
• Calculate risk classification differential changes, including balancing back

• Calculus
• Financial mathematics

• Severity models
• Aggregate models
• Coverage modifications
• Construction and selection of parametric models
• Credibility
• Reserving and pricing for short-term insurance coverages