Finance 550 Numerical Methods & Optimization in Finance

Phil Dybvig
314-398-3196 (cell)

Washington University Olin School

Focus: Applications of Optimization theory and numerical techniques

Optimization is one of the pillars of finance that was inherited from Economics. In this class, we look at financial applications of analytic and numerical optimization. We will define and exemplify different types of optimization problems: nonlinear optimization, concave optimization, linear programming quadratic programming, integer programming, and dynamic programming. Many of the numerical tools were developed in Operations Research. We are limited in scope by the Mini format, but we will talk some about algorithms but mostly about applications.

Essential tools and concepts, up-to-date applications The tools we will discuss have been around a long time and I knew about most of them when I was in graduate school. However, most of the applications are newer and I had a part in developing many of them.

Prerequisites Introductory finance and a thorough knowledge of binomial option pricing are essential. Knowing about continuous-time option pricing is also useful, and will be used in some more advanced optional problmes. is the only formal prerequisite. As in most quantitative courses, students with the strongest math backgrounds will breeze through most easily. This course places more quantitative demands on students than most of our other finance courses.

Feedback Given that I am teaching this material for the first time, feedback is especially useful and appreciated. A good job of pointing out typos, conceptual problems, and other deficiencies of the course can increase your grade at the margin.

Organization of the course The course will be in a traditional lecture format, with problem sets and a final exam.

Course Requirements Grades will be based 70% on the final exam and 30% on the problem sets. Class participation may change a grade near a cutoff, as may useful feedback on the course materials. Understandably, job search or other obligations may occasionally conflict with class. It is your responsibility to find out from your classmates what you miss when you are absent.

Problem Sets The problem sets are available on my web page or through Blackboard (which also points at the web page). Problem sets have several parts. The normal parts without any special label are recommended for all students. Some will have solutions provided for study and learning, and each week one problem will be earmarked to be submitted for grading. The "challengers" are very tough questions intended to stretch the very best students.

Rules for Problem Sets Students are permitted to get help from anyone for the normal and extra-for-experts parts of the homework, but students are required to do their own write-ups and any computer work individually. The challenger questions are strictly individual efforts. All homeworks and related programs should be handed in at the start of the following week's class.

Final Exam The final exam is scheduled on Friday, June 25, during regular class time 6:15-9:15. Usually, my exams are straightforward and if you have done the homeworks yourself and you go to the lectures and study the slides and text you should do well. If you miss the exam for whatever reason or you need to take the exam at another time, I will substitute an oral exam. This avoids even the appearance that someone may have access to exam questions or answers in advance.

Course materials Course materials include a required textbook and slides and problem sets that are available on the web. There is no separate packet.

Transparencies The lectures will be based on transparency slides that are available on the Web, one set of slides per week (with extra introductory lecture 0 the first week). You will probably want to print a paper copy of the slides before each class for cross-reference during class, for study, and for taking notes on. The slides are available from Blackboard or my teaching page on the WEB: or I also invite you to visit my home page and research page:

Textbook The textbook is Optimization Models in Finance by Gerard Cornuejols and Reha Tütüncü. This book was developed for the Carnegie-Mellon multi-disciplinary program in mathematical finance ant it follows a traditional operations-research optimization course with examples from finance and some modern developments. While the authors come from the operations-research tradition, they have consulted with financial economists and there are many good applications.

Here are recommendations about how to time readings with the lectures. In most cases, there is a lot more information in the text than what we need in the course, and there is some information in the course not covered in the book.

Cornuejols and Tütüncü Chapters
Week 11, 5.5, Appendix A
Week 22,3
more to come

Teaching AssistanceWe will be assisted by two OMM PhD students, Xiaole Wu and Ehsan Bolandifar, and one Finance PhD Student, Kangzhen Xie. They all have good backgrounds in mathematics and doctoral level training in finance. Here is their contact information:

Xiaole WuSimon 386314-935-6709
Ehsan BolandifarSimon 286314-489-5143
Kangzhen Xie280B314-935-7155

Of course, you can also direct your questions to me; I recommend e-mail at as an effective way of tracking me down quickly. (Please do not put the e-mail addresses on any web site or mailing list. They are given in graphical form in a feeble attempt to slow down the spammers.)

About you In addition to enrolling through the proper authorities, please send me an e-mail with the following information:

If you enroll and later choose to drop the class, please let me know about that, too, with feedback about why the course didn't work for you.

About me I was previously a tenured full professor at Yale, and I came to Wash U in 1988 in the hope of building a top finance group, which we have done. More information on me is in the chatty blurb at or in my vitae at All of my Web pages can be accessed through my home page.

Feedback Feedback is especially important to me. Written feedback by e-mail is especially useful.

Integrity Students are expected to conform to the Olin School's Code of Conduct.

Summary I invite you to join me in exploring the exciting applications of optimization to finance!