Math 5637 (395) Risk Theory

Fall 2011


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


Take home open book final exam was distributed at the end of class on December 9.  Here are the solutions (corrected on 12-16) and a spreadsheet for some gamma function calculations.  Exam, paper and project grades are here.  Course grades have been posted to the registrar’s system.


Cumulative Assignments (Most recent on top)


Not on Final Exam, but worth looking at: Sec. 11.1-11.4 and exerc. 11.1-11.3, 11.6-11.7, 11.9-11.18

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

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 have started working on at least 4 of them by 10-10.

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

   (In 3, 4, 6, and 22 please follow the instructions exactly or you might not get credit.  3, 4 and 22 are intended to have you learn (by developing them) alternative ways to see concepts treated in the text by integration by parts and in my classroom notes by the surface interpretation.  If all you do integrate is by parts (in any of them) or use the surface interpretation (in 4 or 22) then you have not really developed an alternative way to solve the problem.  The whole point of 6 is the interpretation in terms of stationary population; if you don’t get to that you’ve missed the point of the project. )

 By 12-5 you should be able to consider working on all projects