Math 5637 (395) Risk Theory
MWF 12-12:50 MSB 411
Instructor – James G. Bridgeman
Errata for textbook: http://www.soa.org/files/pdf/edu-loss-models-errata-corrections.pdf
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
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.
Cumulative Assignments (Most recent on top)
(Final)
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
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.)