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 3^{rd} 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.)