MATH 0342 - Actuarial Problem Solving: Probability

Credits: 3

This course develops fundamental concepts of probability in a context of financial risk. A thorough knowledge of single-variable differential calculus is assumed. Topics include probability spaces, calculating probabilities using addition and multiplication rules, independence, combinatorics, conditional probability and Bayes' theorem, measurements of central tendency, percentiles, probability mass and density functions, cumulative distributions, distribution transformations, moment generating functions, expected value and higher moments, variance and coefficient of variation, discrete joint probability functions, method of convolutions, conditional and marginal distributions, covariance and correlation, joint moments, order statistics, the Central Limit Theorem, Chebychev's theorem and Jensen's inequality. Students will work frequently with common distributions including uniform, binomial, Poisson, negative binomial, geometric, hypergeometric, exponential, normal, gamma, beta, lognormal, Pareto, mixed, and bivariate normal. Students will be able to apply these probability concepts to both loss random variables and payment random variables. Students will also explore concepts in insurance such as deductibles, policy limits, inflation, and re-insurance. This course is designed to fully prepare students for the actuarial exams SOA P and CAS 1.

Prerequisites: MATH 0106 and either MATH 0333 or MATH 0340, or permission of instructor.

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