Coursebooks

Optimization methods

Perazzi Elena

English

Remarque

For sem. MA1. Special schedule: see the IF website http://sfi.epfl.ch/mfe/study-plan

Summary

This course presents the problem of static optimization, with and without (equality and inequality) constraints, both from the theoretical (optimality conditions) and methodological (algorithms) point of view. Economics and financial applications are provided. Dynamic optimization is also introduced

Content

Static optimization:

• Univariate and multivariate unconstrained optimization: existence and uniqueness of solutions. Algorithms:Newton¿s method, golden-section search, steepest descent.
• Constrained optimization with equality constraints: Lagrange multipliers and their interpretation.
• Constrained optimization with inequality constraints: Kuhn-Tucker method and duality theory.
• Several examples from economics and finance

Dynamic optimization

• Bellman equation and optimal control problems
• Applications to finance: dynamic portfolio optimization
• Applications to economics: dynamic consumption/saving choice.

Keywords

Optimization program, equality and inequality constraints, Lagrange and Kuhn-Tucker theorems, algorithms, Bellman equation, optimal control.

Learning Prerequisites

Important concepts to start the course

Basic concepts of linear algebra, mathematical analysis and probability.

Learning Outcomes

By the end of the course, the student must be able to:
• Describe optimization programs with and without equality or inequality constraints
• Solve optimization programs with and without equality or inequality constraints
• Describe algorithms adopted to solve such a univariate and multivariate optimization problems.
• Apply different algorithm to financial applications such as portfolio optimization and parameter estimation.
• Solve simple optimal control problems.

Transversal skills

• Use a work methodology appropriate to the task.
• Set objectives and design an action plan to reach those objectives.
• Demonstrate the capacity for critical thinking
• Use both general and domain specific IT resources and tools

Slides.

Assessment methods

The grading will be based on exercises (30%), and (70%) final exam. The final exam is closed-books and closed-notes.

Resources

No

Bibliography

- Brandimarte P., ¿ Numerical Methods in Finance¿, Wiley Series in Economics and Statistics

- Dixit, A. K., "Optimization in economic theory", Oxford University Press, second edition.

- C. P. Simon and L.E. Blume, "Mathematics for Economists", W. W. Norton and Company

- R. K. Sundaram, "A First Course in Optimization Theory", Cambridge University Press.

Notes/Handbook

Slides for each lectures will be provided.

In the programs

• Financial engineering, 2019-2020, Master semester 1
• Semester
Fall
• Exam form
During the semester
• Credits
2
• Subject examined
Optimization methods
• Lecture
1 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks
• Financial engineering, 2019-2020, Master semester 3
• Semester
Fall
• Exam form
During the semester
• Credits
2
• Subject examined
Optimization methods
• Lecture
1 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
8-9
9-10EXTRANEF_126
10-11
11-12
12-13
13-14 EXTRANEF_126
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Lecture
Exercise, TP
Project, other

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• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German