MATH 467/567

Spring 2017

Actuarial Mathematics



Instructor: Yevgeniy Kovchegov
e-mail: kovchegy @math. oregonstate.edu
Office: Kidder 368C
Office Phone No: 7-1379
Office Hours: M 1:30pm - 3:00pm, W 1:00pm - 2:30pm



Place and time: MWF 11:00am to 11:50am, room BEXL 416.

Web materials: Prerequisites: MTH 463/563 or ST 421 or instructor's approval.

Course description: In this class we will study risk theory and foundations of actuarial science from the mathematical models perspective. Specifically, we will learn the mathematics behind insurance systems. We will cover the basics of risk and insurance: risk, loss, claims, net premium, deductibles, aggregate loss, proportional reinsurance, and excess of loss reinsurance.

The course is interdisciplinary in its nature, and is taught by a mathematician experienced in teaching interdisciplinary students. The students with less advanced mathematical preparation will be assigned practical simulation and computational projects for understanding the material.

Syllabus:  PDF file

Homework: TBA



Schedule:
Monday, April 3  Review of probability. Discrete random variables. Expectation, variance, and moments. Moment generating function. Bernoulli random variables. Lecture 1-4 slides (PDF)
Wednesday, April 5  Review of probability. Moment generating function. Independent random variables. Sums of independent random variables. Binomial random variables. Lecture 1-4 slides (PDF)
Friday, April 7  Review of probability. Poisson random variables. Moment generating function of Poisson random variables. Sums of Binomial random variables. Sums of Poisson random variables. Poisson vs Binomial random variables. Lecture 1-4 slides (PDF)
Monday, April 10  Review of probability. Geometric random variables. Moment generating function of geometric random variables. St. Petersburg paradox. Lecture 1-4 slides (PDF)
Wednesday, April 12  Review of probability. Continuous random variables. Standard normal random variables. Moment generating function of standard normal random variables. Lecture 5-9 slides (PDF)
Friday, April 14  Moment generating function of standard normal random variables. Moments of standard normal random variables. Lecture 5-9 slides (PDF)
Monday, April 17  De Moivre - Laplace theorem via moment generating functions. Exponential random variables. Lecture 5-9 slides (PDF)
Wednesday, April 19  Memorylesseness property of exponential and geometric random variables. Gamma random variables. Moment generating functions of exponential and gamma random variables. Lecture 5-9 slides (PDF)
Friday, April 21  Properties of gamma random variables. Poisson process. Lecture 5-9 slides (PDF)


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