Math 5637 (395) Risk Theory

Fall 2010


MWF 12-12:50 MSB 411


Instructor – James G. Bridgeman


instructor's web site

syllabus for the course


Errata for textbook:


What Is Risk Theory?


Maximum Entropy Paper (K. Conrad)    Faa's Formula


Euler Lagrange Equation  Erlang Distribution


EXCEL Example for Convolution (see page 208) 

(note use of the EXCEL functions OFFSET and SUMPRODUCT)


Distribution fitting example (see pp 207-208)


Stop-Loss Example    Stop Loss Example Spreadsheet 


Ruin Theory I   Ruin Theory II


Example of Compound Geometric and Panjer Recursion For Ruin Probabilities


Paper and Projects due 5 PM Monday 12-13, in my mailbox, under my office door, or by email.  (Project #31 could be handed in by 5PM 12-16)


Here is the Final Exam.  Here are Solutions and Solution Spreadsheet.


Grading Worksheet.


Cumulative Assignments (Most recent on top)


Study the Two Ruin Theory Notes above and the spreadsheet example for ruin probabilities

Sec. 11.1-11.4 and exerc. 11.1-11.3, 11.6-11.7, 11.9-11.18

Sec. 10.1-10.2

Study the Stop-Loss Example and Spreadsheet above … be able to do such problems independently

Study the EXCEL examples and distribution fitting examples above and be able to do such calculations independently.

Sec. 9.8-9.12 and exerc, 9.47-9.65, 9.67-9.69

Sec. 9.1-9.7 and exerc. 9.1-9.36

Sec. 6.7-6.13 and 8.6; exerc. 6.10-6.28, 6.32, 8.29-8.34

Use Faa’s formula to calculate the first 4 raw and central moments of the Poisson, Neg. Binomial, and Binomial distributions

Sec. 6.1-6.6 and exer. 6.1-6.9 

Validate (comparing formulas is good enough, but surface interpretation is interesting so you might want to try it) that if X is a log-logistic then the k-th conditional tail moment distribution of X is a transformed beta (or, when γ=1, a generalized Pareto)

Write down a formula for the 3rd moment analogous to Theorem 8.8

Be sure that you can see Theorems 8.3, 8.5, 8.6, 8.7 and 8.8 in terms of the surface interpretation

Sec. 8.1-8.5 and exer. 8.1-8.28 (In chapter 8 try to think in terms of the surface interpretation.  It will simplify everything)

Get going on some projects! To be on pace you should be working on at least 4 of them by 10-8

Sec. 5.3-5.5 and exer. 5.21-5.27

Calculate the first 6 central moments in terms of mean and (a) raw moments (b) cumulants (c) factorial moments

Sec. 5.1-5.2 and exer. 5.1-5.20 (keep a bookmark in appendix A!)

Study the Maximum Entropy paper (download above)

Sec. 4.1-4.2 and exer. 4.1-4.12

Sec. 3.4 and 3.5; exer.3.25 to 3.37 (Beware some misprints in both the text and the solution manual.  See errata!)

Sec. 3.1-3.3 and Exer. 3.1-3.24

Ch. 1&2 and Exer.2.1-2.5 


Project Topics: (pick any eight to submit by end of semester … topics will be added as we go)

See the projects list at Risk Theory Resources

As of 12-10 you should be able to try all projects.  (In 3, 4, 6, and 22 please follow the instructions exactly.  They are intended to challenge your ingenuity.)