Math 5637 (395) Risk Theory

MWF 12:20-1:10 MSB 411

Instructor – James G. Bridgeman

Errata for 3^{rd} edition of the textbook: http://www.beanactuary.org/exams/preliminary/exams/syllabi/Loss_Models.pdf

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

Euler Lagrange Equation Erlang Distribution

EXCEL
Example for Convolution (see page 208 3^{rd} ed. page 146 4^{th}
ed.)

(note use of the EXCEL functions OFFSET and SUMPRODUCT)

Distribution fitting
example (see pp 207-208 3^{rd} ed. pp 145-146 4^{th} ed.)

Stop-Loss Example Stop Loss Example Spreadsheet

Example of Compound Geometric and Panjer Recursion For Ruin Probabilities

Final
Exam Final Exam Solutions Paper,
Project, and Exam Grades

Grades for the course have been
posted with the registrar

**Cumulative
Assignments 3 ^{rd} Edition** (Most recent on top)

(Final – for 12-2)

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. 9.11 and exerc, 9.70 – 9.80

Sec. 9.1-9.7 and exerc. 9.1-9.36

Sec. 6.8-6.10, 6.12-6.13 and 8.6; exerc. 6.14-6.23, 6.32-6.33, 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

If you are not working on at least 6 projects you are behind schedule!

Exer. 6.1-6.3, 6.10-6.13

Sec. 6.1-6.5, 6.7

Exer. 8.11-8.28 (In chapter 8 try to think in terms of the surface interpretation. It will simplify everything)

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. 8.1-8.10 (In chapter 8 try to think in terms of the surface interpretation. It will simplify everything)

Sec. 5.3-5.4 and exer. 5.21-5.26

Exer. 5.11-5.20 (keep a bookmark in appendix A!)

Sec. 5.1-5.2 and exer. 5.1-5.10 (keep a bookmark in appendix A!)

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

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 for 3^{rd} edition. See errata!)

Sec. 3.1-3.3 and Exer. 3.1-3.24 (Refer to Appendix A and B as needed)

**Cumulative
Assignments 4 ^{th} Edition** (most recent on top)

(Final – for 12-2)

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 and exerc. 9.64 – 9.74

Sec. 9.1-9.7 and exerc. 9.1-9.36

Sec. 7.1-7.4, Ch 7 Appendix, and 8.6; exerc. 7.1-7.10, (7)A.11- (7)A12, 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

If you are not working on at least 6 projects you are behind schedule!

Exer. 6.1-6.7

Sec. 6.1-6.6

Exer. 8.11-8.28 (In chapter 8 try to think in terms of the surface interpretation. It will simplify everything)

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. 8.1-8.10 (In chapter 8 try to think in terms of the surface interpretation. It will simplify everything)

Sec. 5.3-5.4 and exer. 5.21-5.26

Exer. 5.11-5.20 (keep a bookmark in appendix A!)

Sec. 5.1-5.2 and exer. 5.1-5.10 (keep a bookmark in appendix A!)

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

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

Sec. 3.1-3.3 and Exer.3.1-3.24 (Refer to Appendix A and B as needed)

Ch. 1&2 and Exerc. 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

By 12-2 you should be able to work on any of projects 1- 30, 32 - 44

(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 is integrate 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. )