MATHS
457: Actuarial Models 1 (4)
Syllabus
- Prerequisite: MATHS 321
- Course
Description:
Loss and frequency distributions, limited expected value, effects of
inflation, parametric and non-parametric models, identification procedures
for insurance company data, bootstrapping, Bayesian analysis, compound
frequency, methods for censored and truncated data, classical and Bayesian
credibility models, experience rating.
- Course
Objective:
Students will apply the statistical concepts that they have previously
encountered to the special problems of insurance products. They will
learn and become comfortable with the methods used for identification of
the most common severity and frequency models used by the actuarial
profession. Students will also become familiar with one or more
computer statistical languages and packages.
- Course
Rationale:
Many problems encountered by actuaries in the insurance industry involve
the analysis of incurred losses or the number of submitted claims for an
insured event. In practice, it is often necessary to find a reasonable and
usable model for the distribution of these random variables. This
course acquaints students with the concepts underlying identification of
parametric statistical models, with special emphasis given to models used
for severity and frequency in the insurance industry.
- The
material covered in this course is directly tested on the third and fourth
professional examinations given by the Society of Actuaries and the
Casualty Actuarial Society.
- Course
Content:
Topics will include parametric and non-parametric models for the
distribution of the amount of an individual loss to a policyholder (loss
distribution), accounting for the effects of inflation in a loss model,
the concept of limited expected value, the distribution of the number of
claims paid by the insurance company (frequency distribution), classes of
frequency models, compound frequency models, applications of maximum
likelihood and method of moments procedures for insurance company data,
computing the variance of parameter estimates through Monte Carlo
procedures (bootstrapping), Bayesian analysis, methods for censored and
truncated data, introduction to classical and Bayesian credibility models,
and the connection between credibility theory and experience rating.
- Course
Format: This
course will be taught using lectures and discussion. A statistical
program or package is required for projects, homework, and take-home
exams. Many examples will be presented, including some problems from
past actuarial exams.
- Methods
of Evaluating Student Performance: Student evaluation may be based on in-class exams,
take-home exams, individual or group projects, homework, and
presentations. The particular methods used and the weight of each
component are at the discretion of the individual instructor.
- Evaluation
of the Course:
The instruction of the course is evaluated by departmental student
evaluations and peer evaluation. The course is reviewed and revised
periodically by the Departmental Undergraduate Programs Committee.
Revised
J. Foley, B. Frye 4/23/04, M. Karls 3/2007