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 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.)
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 3rd 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 3rd 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 3rd edition.)
Sec. 3.1-3.3 and Exer. 3.1-3.24 (Refer to Appendix A and B as needed)
Cumulative Assignments 4th 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 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!)
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