Math 5637 (395) Risk Theory
Fall 2014
MWF 12:20-1:10 MSB 411
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
Grades
on PROJECTS, PAPERS, and EXAMS; COURSE grades have been entered on
Registrar’s system.
Cumulative Assignments 3rd Edition (Most recent on top)
(Final)
Study the Stop-Loss Example and Spreadsheet above … be able to do such problems independently
(For 12-1)
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
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!)
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)
Study the Stop-Loss Example and Spreadsheet above … be able to do such problems independently
(For 12-1)
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
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
By 12-3 you should be able to work on projects 1- 30, 32-45. If you have not started to work on your eight projects by now then you are behind schedule!
(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.)