Welcome#

Course title: “Optimization for Economics and Financial Economics”

  • Elective second year course in the Bachelor of Economics program ECON2125

  • Compulsory second math course in the Master of Economics program ECON6012

The two courses are identical in content and assessment, but final grades may be adjusted depending on your program.

Plan for this lecture#

  1. Organization

  2. Administrative topics

  3. Course content

  4. Self-learning materials

Instructor#

Fedor Iskhakov Professor of Economics at RSE

Timetable#

Face-to-face:

  • Lectures: Thursday 15:30 — 17:30

  • Location: DNF Dunbar Lecture Theatre, Physics Bldg 39A

Online:

  • Echo-360 recordings on Wattle

  • All notes and materials on optim.iskh.me

Face-to-face is strictly preferred

Course web pages#

  • Wattle Schedule, announcements, teaching team contacts, recordings, assignment, grades

  • Online notes Lecture notes, slides, assignment tasks

  • Lecture slides should appear online the previous day before the lecture

  • Details on assessment including the exam instructions will appear on Wattle

Tutorials#

  • Enrollments open on Wattle

Tutorial questions

  • posted on the course website

  • not assessed, help you learn and prepare

Tutorials start on week 2

Tutors#

Wending Liu

Chien Yeh

Prerequisites#

See Course overview and Class summary

What you actually need to know:

  • basic algebra

  • basic calculus

  • some idea of what a matrix is, etc.

≈ content of EMET1001/EMET7001 math course

Focus?#

Q: Is this optimization or a general math-econ course?

A: A general course on mathematical modeling for economics and financial economics. Optimization will be an important and recurring theme.

Assessment#

  • 3 timed open book tests (15% each)

  • Final exam (55%)

The three tests spread out through the semester will check the knowledge of the immediately preceding material. The final closed book in-person exam will cover the entire course.

Questions#

  1. Administrative questions: RSE admin

  • Bronwyn Cammack Senior School Administrator

  • Email: enquiries.rse@anu.edu.au

  • “I can not register for the tutorial group”

  1. Content related questions: please, refer to the tutors

  • “I don’t understand why this function is convex”

  1. Other questions: to Fedor

  • “I’m working hard but still can not keep up”

  • “Can I please have extra assignment for more practice”

Attendance#

  • Please, do not use email for instructional questions\Instead make use of the office hours

  • Attendance of tutorials is very highly recommended
    You will make your life much easier this way

  • Attendance of lectures is highly recommended
    But not mandatory

Comments for lectures notes/slides#

  • Cover exactly what you are required to know

  • Code inserts are the exception, they are not assessable

In particular, you need to know:

  • The definitions from the notes

  • The facts from the notes

  • How to apply facts and definitions

If a concept in not in the lecture notes, it is not assessable

Definitions and facts#

The lectures notes/slides are full of definitions and facts.

Definition

Functions \(f: \mathbb{R} \rightarrow \mathbb{R}\) is called continuous at \(x\) if, for any sequence \(\{x_n\}\) converging to \(x\), we have \(f(x_n) \rightarrow f(x)\).

Possible exam question: “Show that if functions \(f\) and \(g\) are continuous at \(x\), so is \(f+g\).”

You should start the answer with the definition of continuity:

“Let \(\{x_n\}\) be any sequence converging to \(x\). We need to show that \(f(x_n) + g(x_n) \rightarrow f(x) + g(x)\). To see this, note that …”

Facts#

In the lecture notes/slides you will often see

Fact

The only \(N\)-dimensional subset of \(\mathbb{R}^N\) is \(\mathbb{R}^N\).

This means either:

  • theorem

  • proposition

  • lemma

  • true statement

All well known results. You need to remember them, have some intuition for, and be able to apply.

Note on Assessments#

Assessable = definitions and facts + last year level math + a few simple steps of logic

Exams and tests will award:

  • Hard work

  • Deeper understanding of the concepts

In each question there will be a easy path to the solution

Reading materials#

Primary reference: lecture slides

Books:

_images/simon_blume.png _images/sundaram.png _images/stachurski.png

  • “Mathematics for Economists” (1994) by Simon, C. and L. Blume

  • “A First Course in Optimization” (1996) Theory by Rangarajan Sundaram

  • “A Primer in Econometric Theory” (2016) by John Stachurski

Readings are supplementary but will provide a more detailed explanation with additional examples.

  • Each lecture will reference book chapters

Key points for the administrative part#

  • Tutorials start next week, please register before the next lecture

  • Course content = what’s in lecture notes/slides

  • Lecture slides are available online and will be updated throughout the semester

  • Optimization is a recurring theme but not the only topic

What you will learn in the course#

Essentially:

  1. Mathematical foundations

  • elements of analysis

  • elements of linear algebra

  • elements of probability

  1. Optimization theory

  • when solution exists

  • unconstrained optimization

  • optimization with equality constraints

  • optimization with inequality constraints

  1. Further topics

  • Parameterized optimization problems

  • Optimization in dynamics

Further material and self-learning#

  • Each lecture will suggest some material for further reading and learning

  • Today: The Wason Selection Task logical problem

  • Mathematics relies on rules of logic

  • Yet, for human brain applying mathematical logic may be difficult, and dependent on the domain

Please, watch the video and try to solve the puzzle yourself youtu.be/iR97LBgpsl8