UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

Actuarial Science Program

DEPARTMENT OF MATHEMATICS

 

Math 490 / 568

Casualty Actuarial Mathematics

 

 

Fall 2009

 

Rick Gorvett

151 Everitt Lab

 

374 Altgeld Hall

9:30-10:50 am TuTh

 

Phone: 244-1739

 

 

 

Office Hours:

3-4 pm Tues and 2-4 pm Wed, or by appointment

 

 

E-mail: gorvett@uiuc.edu

 

Required Text: Foundations of Casualty Actuarial Science by Casualty Actuarial Society (4th Edition)

 

See below for Class Summaries (including assignment postings) and Current Events

 

Course Overview

 

This course provides an introduction to property/casualty actuarial science by exploring its mathematical, financial, and risk-theoretical foundations. Specific topics include risk theory, loss reserving, ratemaking, risk classification, credibility theory, reinsurance, financial pricing of insurance, and other special issues and applications. These foundational concepts should be useful in any actuarial or financial mathematics environment. Many of the readings assigned in this course appear on one or another of the advanced professional examinations of the Casualty Actuarial Society (CAS), in particular exams 5 and 6.

 

Throughout the semester, a number of practicing casualty actuaries will be invited to speak in class on various relevant topics and applications. In addition, real-world-type property-casualty actuarial projects will be undertaken. Mentoring relationships with practicing actuaries may also be organized, to provide students with insights into the realities of the actuarial profession, and perhaps also to help with class projects or assignments.

 

Accessibility Statement

 

To ensure that disability-related concerns are properly addressed throughout the semester, students with accessibility issues who require reasonable accommodations to participate in this class are asked to see me right away.

 

Honors Projects

 

For those involved in a Campus or College honors program, such as James Scholar, you are welcomed to perform an honors project in association with this class. Such a project would involve an opportunity for undergraduate research relevant to actuarial science. Please let Prof. Gorvett know of your interest in the first few weeks of the class.

 

Grading

 

Course grades will be determined based on the following weights:

 

Homework Assignments

15 %

Group Project 1

10 %

Group Project 2

10 %

Other Assignments/Exercises

5 %

Exam 1

20 %

Exam 2

20 %

Final Exam (Exam 3)

20 %

 

Exams may not be made-up or taken at different times, except in an extreme emergency. In general, the grade weight for a missed exam (provided there is a valid excuse) will accrue equally to any remaining exams. A missed homework or other assignment/exercise also may not be made up. Class attendance is expected and required. Excessive absences may result in a lower grade than that earned according to the formula above.

 

Please note that the final exam schedule is prescribed by the university; in general, instructors are not permitted to change the final exam timing of their courses.

 

Graduate students taking this class for four hours of credit will be required to complete one additional project. Performance on this project may impact the overall grade.

 

Key Dates

 

The following are key dates associated with this course:

 

First day of class

Tuesday, Aug. 25

Exam 1

Thursday, Oct. 1

Exam 2

Thursday, Nov. 5

Last day of class

Tuesday, Dec. 8

Final exam (Exam 3)

8 am, Friday, Dec. 11

 

 

Other Important Information

 

Sep. 17, 2009

Registration Deadline for Exam 3L (Casualty Actuarial Society) in Oct. 2009

Sep. 24, 2009

Registration Deadline for:

-Exam 4/C in Nov. 2009

-Exam 3F/MFE in Nov. 2009

-Exam MLC in Nov. 2009

Oct. 8, 2009

Registration Deadline for Exam 1/P in Nov. 2009

Oct. 22, 2009

Registration Deadline for Exam 2/FM in Dec. 2009

Oct. 27, 2009

Exam 3L (Casualty Actuarial Society)

Nov. 2, 2009

Exam 3F/MFE

Nov. 3, 2009

Exam MLC (Society of Actuaries)

Nov. 3-9, 2009

Exam 4/C (CBT)

Nov. 18-30, 2009

Exam 1/P (CBT)

Dec. 1-8, 2009

Exam 2/FM (CBT)

 

 

Class Summaries

 

Date

General Topic

Specific Class Topics

Assignments

Reading

Other Items / Links

Aug 25

Introduction and Overview

Syllabus and class overview.

Insurance industry.

Casualty actuaries.

 

FCAS, Ch 1

Class Lecture Notes (1)

Casualty Actuarial Society

Aug 27

Risks and Risk Theory

Types of risks and insurance policies.

Legal environment.

Surplus and risk theory.

 

FCAS, Ch 2

Class Lecture Notes (2)

Sep 1

Economics and Insurance Markets

Underwiting cycle.

Characteristics of insurance markets.

Macroeconomic context.

 

Boor Papers:

(1) Macroeconomic View

(2) Economic Cycle

Class Lecture Notes (3)

Sep 3

Loss Reserving

Data.

Loss reserving issues.

Loss development technique.

Student current event presentations begin next class

FCAS, Ch 5

Class Lecture Notes (4)

Sep 8

Loss Reserving (cont.)

Loss development technique (cont.).

HW#1

ICA#1

FCAS, Ch 5

Class Lecture Notes (5)

Sep 10

Loss Reserving (cont.)

BF and ELR techniques.

Diagnostics.

Reserving issues.

Accounting issues.

 

CAS Statement of Loss Reserving Principles

Blanchard Study Note

 

Class Lecture Notes (6)

ELR and B-F Examples

Sep 15

Ratemaking

Overall concept.

Pure premium method.

Loss ratio method.

 

FCAS, Ch 3

Class Lecture Notes (7)

HW#1 Solutions

HW#1 Spreadsheet

Sep 17

Ratemaking (cont.)

Trend and development.

Basic versus total limits.

Parallelogram method for premium.

HW#2

FCAS, Ch 3

Class Lecture Notes (8)

Sep 22

Ratemaking (cont.)

Putting together the elements of the ratemaking process.

 

FCAS, Ch 3

Class Lecture Notes (9)

Sep 24

Risk Classification

Concepts and principles.

Calculations of new base rates and relativities.

 

FCAS, Ch 6

Class Lecture Notes (10)

Sep 29

Review for Exam # 1

Risk classification problems.

Review for Exam # 1.

 

 

HW#2 Solutions

Oct 1

Exam # 1

151 Everitt Lab.

Open book, open note.

Any type of calculator.

Regular class time.

 

 

 

Oct 6

Individual Risk Rating

Hand back and review Exam # 1.

Individual risk rating.

 

FCAS, Ch 4

Class Lecture Notes (11)

Oct 8

Claims Made Coverage

Occurrence vs claims made.

Loss triggers.

Retroactive date.

Tail coverage.

HW#3

 

Class Lecture Notes (12)

 

Oct 13

Reinsurance

Sample problems on claims made coverage.

Reinsurance intro.

Proportional vs excess.

 

FCAS, Ch 7

Class Lecture Notes (13)

 

Oct 15

Reinsurance (cont.)

Functions of reinsurance.

Reinsurance terminology and issues.

Project 1

Project 1 Data

Project 1 LDF

ICA#2

FCAS, Ch 7

Class Lecture Notes (14)

HW#3 Solutions

 

Oct 20

Reinsurance (cont.)

Reinsurance calculations.

 

FCAS, Ch 7

 

Oct 22

Reinsurance (cont.)

Reinsurance calculations.

ICA#3

FCAS, Ch 7

 

Oct 27

Increased limits factors

Exposure rating.

ILFs.

ICA#4

FCAS, Ch 7

Class Lecture Notes (15)

Oct 29

Credibility

Classical credibility.

Buhlmann and Bayesian credibility.

HW#4

FCAS, Ch 8

Class Lecture Notes (16)

Nov 3

Review for Exam # 2

Go over problems as part of review.

 

 

Problems for Review

Solutions to Review Problems

HW#4 Solutions

Nov 5

Exam # 2

151 Everitt Lab.

Open book, open note.

Any type of calculator.

Regular class time.

 

 

 

Nov 10

Finance and Financial Applications

Handed back and went over Exam # 2.

Finance background.

Target total rate of return.

Graduate Project

FCAS, Ch 9

Class Lecture Notes (17)

Nov 12

Finance and Financial Applications (cont.)

CAPM applied to insurance ratemaking.

Discounted cash flow approach to insurance ratemaking.

ICA#5

FCAS, Ch 9

Class Lecture Notes (18)

Nov 17

Finance and Financial Applications (cont.)

Option pricing theory as applied to insurance ratemaking.

Project 2

Project 2 Data

ICA#6

FCAS, Ch 9

 

Nov 19

Presentation by State Farm Research Center

 

 

 

 

Dec 1

Dynamic Financial Analysis

Integrated modeling of the underwriting and investment functions of an insurer.

HW#5

FCAS, Ch 10

Class Lecture Notes (19)

Sample Calculations for Project 1

Dec 3

Enterprise Risk Management

Holistic risk management of a firm.

 

FCAS, Ch 10

 

Dec 8

Presentation by Allstate Insurance

 

 

 

HW#5 Solutions

Dec 11

Final Exam

151 Everitt Lab.

Open book, open note.

Any type of calculator.

8-10 am.

 

 

 

 

 

Current Events

 

Date

Current Event Topic

Link (if available)

Comments / Issues

Aug 25

More Energy Firms Go Uninsured

- WSJ, 8/24/09, p. B2.

 

- Many companies involved with Gulf coast energy (including offshore oil rigs) are going self-insured this hurricane season.

- Rate increases and/or drops in insurance coverage availability are causes.

- But enhanced regulation and technology since Hurricane Katrina may aid risk management and promote loss reduction.

Sep 1

Insuring your fantasy sports investment

http://fantasysportsinsurance.com

 

- Claim that their product will protect your investment in a fantasy sports league in the event of key player injury.

- (Appearance on this class website does not represent an endorsement of the product.)

Sep 1

Hospitals Own Up to Errors

- WSJ, 8/25/09, p. D1

Article

- Some hospitals are hoping to reduce lawsuits over medical errors by being more open about those errors.

- Communicating and working with the families.

- A variety of safety measures are being considered and adopted.