Math 395 – Risk Theory

Fall 2006

Classes:  1:00 – 1:50 MWF                            Instructor: James Bridgeman, FSA

                 MSB 315                                                    MSB 408   phone (860) 486-8382

Office hours: 10:00 – 12:00 M                         

                       10:00 – 12:00 Th               

                         2:00 –  3:00 Th/F

                      Or by appointment

Course Homepage:   


Context for the Course

Partial Preparation for CAS Exam 4/ SOA Exam M (Actuarial Models)

(Tuesday November 7)

or SOA Exam C (as revised for Spring 2007)


Specific Course Content

Claim Risk Models and Ruin Models


Required Texts

Klugman, et al.: Loss Models: From Data To Decisions (second edition),

Solutions Manual To Accompany Loss Models second edition

 Students also will be responsible for material not in the text, presented in class


Additional Study Material (not required but might be helpful)

Batten & London: A Guide for the Actuarial Student

Bowers, et al.: Actuarial Mathematics (Second Edition)

Gauger: ACTEX Study Manual for Exam 3 (Vols. I and II)

 Panjer & Willmot: Insurance Risk Models

Ross: Introduction to Probability Models (Eighth Edition)

Ross: Simulation (Third Edition)

Society of Actuaries: Study Note Package for Exam M

Casualty Actuarial Society: Study Note Package for Exam 4


For Future In–Depth Study

(well beyond society exam or course requirements)

Kleiber & Kotz: Statistical Size Distributions in Economics and Actuarial Sciences

Daykin, et al.: Practical Risk Theory for Actuaries

de Vylder: Advanced Risk Theory -- a self-contained introduction

Asmussen: Ruin Probabilities

Willmot & Lin: Lundberg Approximations for Compound Distributions with Insurance Applications


Grading: 4 Take-Home Tests 40%; Final Exam 35%; Paper and Project(s) 25%


the syllabus and grading plan are subject to change with appropriate notice to the class


 Intended Pace for Math 395


Week of …




Aug. 28

Moments, Surface Interpretation, Modified Distributions

Ch. 2, Sec. 3.1-3.2, Class Notes

Sept. 4

Generating Functions, Faa’s Formula,

Severity Distributions

Sec. 3.3, 4.1-4.2, Class Notes

Sept. 11

Tail Weight, Creation of  Severity Distributions and Relations Among Them, Maximum Entropy

Sec. 4.3-4.4, Class Notes

Sept. 18

Creation of Severity Distributions and

Relations Among Them, Coverage Modifications

Class Notes, Sec. 4.5, 5.1-5.5

Sept. 25

 Test #1, Frequency Distributions, (a,b,0)

Sec. 4.6.1-4.6.5, Class Notes

Oct. 2

(a,b,1), Compound Frequency Distributions

Sec. 4.6.6-4.6.8, Class Notes

Oct. 9

Mixed Frequency Distributions, Exposure, Deductibles

Sec. 4.6.9-4.6.11, 5.6

Oct. 16

Test #2, Aggregate Claim Distributions, Model Choices, Compound Models

Sec. 6.1-6.4

Oct. 23

Computing Aggregate Claims, Recursion Method, Coverage Modifications

Sec. 6.5-6.7, Class Notes

Oct. 30

Other Computing Methods, Ruin Models

Sec. 6.8-6.10, 7.1-7.2

Nov. 6

Test #3, Discrete Time Ruin Model

Sec. 7.3, Class Notes

Nov. 13

Continuous Time Ruin Model:

Properties and Probabilities

Sec. 8.1-8.2, Class Notes

Nov. 27

Continuous Time Ruin Model: Distributions

Sec. 8.3-8.5, Class Notes

Dec. 4

Test #4, Project Reviews


Final Exam TBD week of Dec. 10 - 15


the syllabus and grading plan are subject to change with appropriate notice to the class.