Math 5637 (395) Risk Theory

Fall 2015

MWF 12:20-1:10 MSB 415

Instructor - James G. Bridgeman

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

Ruin Theory I----Ruin Theory II

Example of Compound Geometric and Panjer Recursion For Ruin Probabilities

AS STATED IN SYLLABUS, PAPERS AND
PROJECTS ARE DUE MON. 12-14. DUE BY 5
PM, UNDER MY DOOR, IN MY MATH MAILBOX OR ELECTRONICALLY.

FINAL
EXAM: SOLUTIONS GRADING WORKSHEET course grades posted on the
registrar’s site.

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

(Final)

Read for background only Ruin Theory I & II above

Study the Stop-Loss Example and Spreadsheet above … be able to do such problems independently

Study the EXCEL example 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

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

Write me what distribution you have selected for your paper!

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!)

Study the Maximum Entropy paper (download above)

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 3^{rd} edition.)

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)

Read for background only Ruin Theory I & II above

Study the Stop-Loss Example and Spreadsheet above … be able to do such problems independently

Study the EXCEL example 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

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!)

Study the Maximum Entropy paper (download above)

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

(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) 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 do not get to that you
have missed the point of the project.)

Finally, you should be able to work on Projects 1 – 47