Numerical Methods and Optimization in Finance, FIN 550

Philip H. Dybvig
Washington University in Saint Louis


You have probably seen your grades on WebStac, and here is some more information. Competition was fierce on the exam and in the course. Seven of the students scored over 100 on the exam -- maybe I made it too easy or maybe this is just a very strong set of students. The smallest score on the exam was 80. Everyone lost at least some points on the TRUE-FALSE questions (correct answers all FALSE), and seven students solved the bonus problem. Generally, everyone did well on the homework and some people got a modest amount of extra credit for challengers.

Here are the exam and answers: exam pdf size 39K exam answers pdf size 69K

The final exam is coming Thursday, Dec. 13, 1:00-4:00 in Simon 106. For the exam, you are not permitted to have access to notes or any electronics, including cell phones, computers, mp3 players, iPads etc. All of these devices are computers that can be used to store information that can give an unfair advantage and most allow communications which also could be used for cheating. I want to make sure there is not even an appearance of cheating in the class.

To help in your study, here are some practice exams. All are from course offerings a little different than the current version, but the first exam (from last year) is on almost the same material. All of the exams should give you a good picture of the sort of exam I write. In general, my exams are straightforward and there are no trick questions, and you should do well if you have a good command of the material. However, we have covered a lot in the class and the exam will only be easy if you are really on top of things.

Practice exams
...practice exam 1 pdf size 37K
...practice exam 1 answers pdf size 64K
...practice exam 2 pdf size 37K
...practice exam 2 answers pdf size 64K
...practice exam 3 pdf size 39K
...practice exam 3 answers pdf size 51K

Once you are completely on top of the material, you can look at this set of three alternative solutions to one of the bonus questions. Don't waste your time on this if you are still working on the basic material.
...practice exam 1 bonus question solutions pdf size 38K

Welcome to Financial Optimization! This course introduces optimization models that are pervasive in financial theory and practice, with a focus on the tools that are useful in practice. The concepts, tools and applications promise to make this a great term!


I recommend that you print a set of slides before class for taking notes and solving in-class exercises. One topic corresponds to a week or so more. I will not necessarily be following the slides very closely, so you should find out from a classmate who takes good notes what you missed if you are not in class.

Review yourself, as needed:
...univariate calculus review pdf slides size 56K
...matrix algebra ppt slides size 1184K
...eigenvalues and eigenvectors pdf slides size 50K
...derivatives and chain rule using vectors and matrices ppt slides

Week 1: Probability Review and Introduction to Optimization
...Probability, part 1 pdf slides size 96K
...Probability, part 2 pdf slides size 42K
...Optimization pdf slides size 79K
...Problem Set 1, due Nov. 6 pdf size 30K
...Problem Set 1, answer to problem 2 pdf size 28K

Week 2: Constrained and Unconstrained Optimization
...Kuhn-Tucker Conditions pdf notes size 38K
...single-period finance models pdf paper size 220K
...Problem Set 2, due Nov. 13 pdf size 36K
...Problem Set 2, answer to problem 1 pdf size 31K

Week 3: Linear Programming, Duality, and the FTAP
...pdf slides size 38K
...pdf slides size 89K
...Problem Set 3, due Nov. 27 pdf size 25K
...Problem Set 3, answer to problems 1 and 3 pdf size 35K

Week 4: Ordinary Differential Equations (2 lectures) ppt slides size 1192K
...numerics ppt slides size 1256K
...Problem Set 4, due December 4, pdf size 18K
(no solved problems this week; see the slides for similar solved problems)

Week 5: Markov Switching Models
...eigenvalues and eigenvectors pdf slides size 50K
...regime-switching models pdf slides size 58K
...Problem Set 5, not for handing in pdf size 33K
...Problem Set 3, answer to problems 1 and 3 pdf size 41K

Week 6: X-treme Review (based on previous slides)