Math 5637 (395) Risk Theory

Fall 2013

MWF 12:20-1:10 MSB 411

Instructor – James G. Bridgeman

syllabus for the course

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

What Is Risk Theory?

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

(note use of the EXCEL functions OFFSET and SUMPRODUCT)

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

Example of Compound Geometric and Panjer Recursion For Ruin Probabilities

Grades for the course have been posted with the registrar

Cumulative Assignments 3rd 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 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. 8.1-8.10 (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

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 3rd edition.  See errata!)

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

Ch. 1&2 and Exer.2.1-2.5

Cumulative Assignments 4th 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 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. 8.1-8.10 (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

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. )