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

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)

(Final)

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 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 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

**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