FE646 Optimization Models and Methods in Finance

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Course Catalog Description

Introduction

This course concerns making sound financial decisions in an uncertain world. Increasingly, financial decision-makers are depending on optimization techniques to guide them in their decisions. This course introduces the approach of modeling financial decisions as optimization problems and then developing appropriate optimization methodologies to solve these problems. The course discusses the main classes of optimization problems encountered in financial engineering: linear and nonlinear programming, integer programming, dynamic programming, stochastic programming, and robust optimization. Recent topics about portfolio optimization arising in behavior finance will also be discussed in the later part of the course.

The course will also emphasize effective modeling, the use of modeling languages, such as AMPL1, and the use of commercial solvers for solving financial optimization problems.

Campus Fall Spring Summer
On Campus X X
Web Campus X X

Instructors

Professor Email Office
Zhenyu Cui
zcui6@stevens.edu Babbio 514



More Information

Course Description

This course concerns making sound financial decisions in an uncertain world. Increasingly, financial decision-makers are depending on optimization techniques to guide them in their decisions. This course introduces the approach of modeling financial decisions as optimization problems and then developing appropriate optimization methodologies to solve these problems. The course discusses the main classes of optimization problems encountered in financial engineering: linear and nonlinear programming, integer programming, dynamic programming, stochastic programming, and robust optimization. Recent topics about portfolio optimization arising in behavior finance will also be discussed in the later part of the course.
The course will also emphasize effective modeling, the use of modeling languages, such as AMPL1, and the use of commercial solvers for solving financial optimization problems.

Course Outcomes

• Cultivate a basic understanding of the optimization methodologies used in financial decision making;

• Understand how to formulate financial optimization programs using the tools of mathematical programming;

• Understand how to select the optimization technique most appropriate for a given financial optimization problem;


Course Resources

Textbook

• Optimization Methods in Finance, by Cornuejols and Tutuncu, Cambridge University Press (2007), ISBN: 978-0521861700

• AMPL: A Modeling Language for Mathematical Programming, by Robert Fourer, David M. Gay, and Brian W. Kernighan, Second edition, Cengage Learning (2002), ISBN 0-534-38809-4 available for free at http://ampl.com/resources/the-ampl-book/chapter-downloads/

Additional References

• The textbook Convex Optimization, by S. Boyd and L. Vandenberghe can be used for additional readings on some optimization topics. It is available for free from http://web.stanford.edu/~boyd/cvxbook/

• Handbook of Probability, by Ionut Florescu and Cyprian Tudor, 1st edition, Wiley, 2013, ISBN: 0470647272. This is for background study and helpful for basic probabilistic concepts.

• For the recent area of behavior portfolio choice and optimization, refer to http://people.maths.ox.ac.uk/zhouxy/article.htm



Grading

Grading Policies

• There will be 3 or 4 homework assignments (each weighted equally toward your final homework grade) during the course of the semester. You will have about two or three weeks to finish each assignment.

• Only use the “.pdf” format for submitting assignment files. You should be able to transform any document into a pdf file. You can use Adobe acrobat - should be free to Stevens students as far as I know (please call the students help desk), or a simple alternative is to use a pdf printer driver. I write all my documents in LATEX, and that typesetting program produces pdf files. A simple alternative (using any typesetting program) would be to search on Google for a driver that would print to a pdf file. Such drivers are generally free.

• For homework with computer exercises, along with your written answers to the question, give in appendix your commented code as well as the output of your code when you run it.

• Late assignments will not be accepted under any circumstances without prior notice and permission of the instructor. If outside circumstances are affecting your ability to perform in the course, you must contact me before you fall behind.

• An approximate grading scheme is as follows: 1. Homework (each weighted equally toward your final grade): 50%; 2. Final Exam: 50%.


Lecture Outline

Topic Reading
Week 1 Introduction, AMPL language Ch.1 in [1] and Ch.1 in [2]
Week 2 Linear Programming Ch.2 in [2]
Week 3 Arbitrage Detection and Introduction to Portfolio Ch.4 and Ch.8 in [1]
Week 4 Quadratic Programming: Markowitz Portfolio Selection Ch.8 in [1]
Week 5 Nonlinear Programming, Interior Point Method. 1st HW due Ch. 5 and Ch. 7 in [1]
Week 6 Recap of Key Results. Ch. 1, 2, 4, 5, 7, 8 in [1].
Week 7 Integer programming Ch. 11 in [1]
Week 8 Dynamic Programming 2nd HW due Ch. 13, 14, 15 in [1]
Week 9 Stochastic Programming Ch. 16 in [1]
Week 10 Further Stochastic Programming Ch. 16, 17 in [1]
Week 11 Robust Optimization 3rd HW due Ch. 19, 20 in [1]
Week 12 Behavior Portfolio Choice: introduction to behavior finance In Class Slides and Notes
Week 13 Behavior Portfolio Choice: quantile formulation and rank-dependent utility In Class Slides and Notes
Week 14 Behavior Portfolio Choice: portfolio selection under cumulative prospect theory 4th HW due In Class Slides and Notes