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Mathematics 383, Credibility Theory and Loss Distributions, Spring 2001

Illinois State University Mathematics Department
All class materials are available on Canvas

Instructors

Dr. Krzysztof Ostaszewski , FSA , CFA ., MAAA
Actuarial Program Director
Office: Stevenson Hall, room 313G.
Telephone: 309-438-7226. Fax: 309-438-5866.
Toll-free voicemail: 800-MY-YAHOO box 5202441757. Internet fax: 520-244-1757
E-mail: krzysio@ilstu.edu

Classes Meet

Mondays and Wednesdays 4:30-5:50 p.m., in Stevenson Hall, room 310.

Office Hours

Mondays and Wednesdays 1:00-2:00 p.m. Please ask for an appointment at other times.

Textbooks

Loss Models: From Data to Decisions, by Stuart A. Klugman ., Harry H. Panjer and Gordon E. Willmot , published in 1999 by John Wiley and Sons, Inc . Errata for the book is posted here . Supplementary textbook: ACTEX Study Manual for SOA Course 3 and CAS Exam 3, Volume II (Aggregate Loss Models, Stochastic Processes, and Simulation), 2000 Edition ISBN 1-56698-370-3, by Michael A. Gauger.

Objective

The objective of this class is to help you learn about actuarial models of loss contingencies (i.e., financial random variables dependent on losses to insured property). We will cover topics such as: loss distributions, frequency distributions, aggregate loss models, credibility theory, long term models. These actuarial models are tested on the Casualty Actuarial Society /Society of Actuaries Course 3 examination, and form a key part of modern actuarial science.
Here is the actual material from loss contingencies (i..e., other than life contingencies material covered in Mathematics 380) covered on the Course 3 examination:

  • Loss Models: From Data to Decisions, Sections 1.3, 1.4, 2.1, 2.2 (Definitions 2.10, 2.11, 2.12, 2.13 only), 2.6 (pp. 74-77, 83 only), 2.7.1, 2.7.2 (excluding Example 2.40 and following), 2.7.3, 2.10 (excluding 2.10.1 and following), 3.1, 3.2.1-3.2.2, 3.3.1-3.3.2, 3.4.1, 3.5 (through first full paragraph on p. 222), 3.7 (excluding Example 3.15, Theorem 3.4, Example 3.18 and following), 3.10.1 (excluding Example 3.34 and following), 3.10.2 (excluding Example 3.38 and following), 4.1-4.3, 4.5, 4.6 (excluding Theorem 4.4 and Sections 4.6.2-4.6.5), 4.8, Sections 6.2.3, 6.3.1, 6.3.2.1.
  • Ross, S.M., Introduction to Probability Models (Seventh Edition), 2000, Academic Press, San Diego, Sections 2.8, 4.1-4.4, 4.5.1, 4.6, 5.3-5.4, 10.1-10.3.
  • Bowers, N.L.; Gerber, H.U.; Hickman, J.C.; Jones, D.A.; and Nesbitt, C.J., Actuarial Mathematics (Second Edition), 1997, Society of Actuaries, Chapter 13 (excluding autoregressive discrete-time model and Appendix).
  • Ross, S.M., Simulation (Second Edition), 1997, Academic Press, San Diego, Sections 3.1, 4.1-4.3, Chapter 5 (excluding 5.3 and 5.5).

Of the above, the material from Ross’ book is covered in probability and statistics classes, and in some sections of Loss Models which we will cover. Actuarial Mathematics book material is also covered in Loss Models chapter 6, and we will cover that chapter. If you prepare yourself for the Course 3 examination , you should read those required texts. You can ask questions about them in this class freely.

Grading

There will be five tests. You can have a make-up test, but a make-up will be made intentionally at least 20% more difficult. The best three of your five tests will count as 1/3 of your grade each. The grading scale will be as follows: 80% or better — A, 70% to 80% — B, 60% to 70% — C, 50% to 60% — D, below 50% — F. You will also receive up to 20% extra credit for quizes which will be given in many classes, as indicated in the schedule below. While the grading scale may appear liberal, it is justified by the level of difficulty of the material.

Other issues

You are expected to be in class, be prepared and able to contribute to the discussion.  The classroom is a place of learning and showing respect for others at all times.

Schedule of classes

  • Wednesday, January 17, 2001. Chapter 1: A Model-Based Approach to Actuarial Science.
  • Monday, January 22, 2001. Chapter 2: Loss Distributions — Models for  the Amount if a Single Payment.
  • Wednesday, January 24, 2001. Chapter 2: Loss Distributions — Models  for the Amount if a Single Payment. Quiz 1 .
  • Monday, January 29, 2001. Chapter 3: Frequency Distributions — Models   for the Number of Payments. Quiz 2 .
  • Wednesday, January 31, 2001. Chapter 3: Frequency Distributions — Models   for the Number of Payments. Quiz 3 .
  • Monday, February 5, 2001. Chapter 3: Frequency Distributions —  Models for the Number of Payments. Quiz 4 .
  • Wednesday, February 7, 2001. Review.Monday, February 12, 2001. Test No. 1, covering Chapters 1-3.
  • Wednesday, February 14, 2001. Discussion of Appendix D and Appendix H.Monday, February 19, 2001. Chapter 4: Aggregate Loss Models.
  • Wednesday, February 21, 2001. Chapter 4: Aggregate Loss Models. Quiz 5 .Monday, February 26, 2001. Chapter 4: Aggregate Loss Models. Quiz 6 .
  • Wednesday, February 28, 2001. Chapter 4: Aggregate Loss Models. Quiz 7 .
  • Monday, March 5, 2001. Chapter 5: Credibility Theory (not on the tests,   books exercises can be turned in for bonus points).
  • Wednesday, March 7, 2001. Chapter 5: Credibility Theory (not on the tests, books exercises can be turned in for bonus points). Quiz 8 .
  • Monday, March 19, 2001. Chapter 5: Credibility Theory (not on the tests,  books exercises can be turned in for bonus points). Quiz 9 .
  • Wednesday, March 21, 2001. Chapter 6. Long-Term Models.Monday, March 26, 2001. Review.
  • Wednesday, March 28, 2001. Test No. 2, covering Chapters 1-4 .
  • Monday, April 2, 2001. Chapter 6. Long-Term Models. Quiz 10 .
  • Wednesday, April 4, 2001. Chapter 6. Long-Term Models. Quiz 11 .
  • Monday, April 9, 2001. Chapter 6. Long-Term Models. Quiz 12 .
  • Wednesday, April 11, 2001. Chapter 6. Long-Term Models. Quiz 13 .
  • Monday, April 16, 2001. Review.Wednesday, April 18, 2001. Review.
  • Monday, April 23, 2001. Review.
  • Wednesday, April 25, 2001. Extra test .
  • Monday, April 30, 2001. Test No. 3 , comprehensive.
  • Wednesday, May 2, 2001. Test No. 4 , comprehensive.
  • Monday, May 7, 2001, 3:10 p.m. — 5:10 p.m. Test No. 5 (final) , comprehensive.

All information contained here is, to our best knowledge, correct, but it is merely a representation, and should not be considered to be any form of professional advice. This electronic publication should not be misconstrued as the official position of Illinois State University, or its Department of Mathematics. We are glad to provide as much information as possible here, but we kindly ask that in any decision related to matters listed here you seek additional counsel and information. Comments on this Home Page are welcome and should be sent to Dr. Krzysztof Ostaszewski  at his e-mail address: krzysio@ilstu.edu.

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