AMS 410, Actuarial Mathematics

Catalog Description: Reviews relevant mathematical topics in the context of risk assessment and insurance for the first actuarial examination.

Prerequisite: AMS 311 

3 credits

Textbook: ACTEX P/1 Study Manual, 2010 Edition, by Samuel A. Broverman, Ph.D., ASA
ISBN# 9781566987455

Actuarial Exam: The course is a review for the first actuarial exam, Exam P, of the Society of Actuaries . AMS 311 covers the material on Exam P in a traditional mathematical presentation of probability theory. AMS 410 revisits this material in the form of practice questions for Exam P. For more details about actuarial preparation at Stony Brook see Actuarial Program 

THIS COURSE HAS NOT BEEN OFFERED IN RECENT YEARS

Topics:
1. General probability: 8 hours
2. Discrete distributions: 7 hours
3. Continuous distributions: 9 hours
4. Multivariate distributions and transformation: 9 hours
5. Risk management: 3 hours
6. Mid-Term Test and Review: 6 hours

 

Learning Outcomes for AMS 410, Actuarial Mathematics

1.) Demonstrate an understanding of Set Theory and basic Probability Theory concepts:
        * apply DeMorgan’s laws, Distributive laws, inclusion-exclusion principle and other set operations;
        * apply the axioms of probability to calculate certain probabilities;
        * conditional probability;
        * apply the law of total probability and Bayes’ theorem;
        * understand concepts such as independent events & mutually exclusive events.

2.) Understand basic combinatorial principles:
        * understand the difference between permutations and combinations;
        * learn useful techniques, such as counting the number of elements in the complement of a set.

3.) Understand concepts in random variables and corresponding univariate probability distributions:
        * understand the difference between a discrete random variable and a continuous random variable;
        * understand properties of probability mass functions, probability density functions, and cumulative distributions;
        * compute expectation, variance, moment generating functions;
        * apply frequently used discrete distributions (discrete uniform, Bernoulli, binomial, Poisson, geometric, hypergeometric, multinomial);
        * apply frequently used continuous distributions (uniform, normal, exponential, gamma).

4.) Understand and apply multivariate distributions:
        * compute multiple integrals;
        * compute probabilities, expectation, variance, covariance, moment generating functions;
        * find marginal and conditional distributions;
        * understand properties associated with two independent random variables;
        * use of double expectation and law of total variance.

5.) Use of functions and transformations of random variables:
        * compute distribution of a function of a random variable whose distribution is known;
        * compute distribution of a function of two random variables, whose joint distribution is known;
        * apply the convolution method to a sum of continuous random variables, and a sum of discrete random variables;
        * apply the central limit theorem.

6.) Understand risk management:
        * understand the concept of a loss random variable;
        * understand and apply various policies (ordinary deductible, franchise deductible, disappearing deductible, policy limit).