Norman Schürhoff HEC – University of Lausanne Extranef 228 CH-1015 Lausanne Switzerland

October 24, 2006 Syllabus

Mathematics for Economics and Finance

M.S. Economics, M.S. Finance

Period 4.1, Fall 2006

Course Essentials:

Credits: 6

Instructor: Norman Schürhoff

Office: Extranef 228

Phone: 692-3447

Email: Norman.Schuerhoff@unil.ch

Course Website: http://www.hec.unil.ch/schuerhoff/teaching

User: student06 Password: winter

Teaching Assistants: Zhihua (Cissy) Chen (Zhihua.Chen@unil.ch)

Natalia Guseva (nguseva@unil.ch)

Course Hours:

Classes: TU 8:30AM – 12PM, Nef 272

WE 8:30AM – 12PM, Ant 1129

Exercises: FR 3PM – 5PM, Pol C-334

Office Hours: FR 1PM – 3PM

MO 8:30AM – 10:30AM (Cissy)

TH 8:30AM – 10:30AM (Natalia)

Course Objectives:

The course provides an introduction to the mathematical theories and methods used in modern economics and finance. The objective of the course is to equip students with the mathematical toolkit required for later coursework.

Course Organization:

• Fall semester (Oct 24 – Dec 6), 56 hours over 7 weeks

• Lectures and exercise sessions

• Midterm and final exam

Course Outline:

1. Real Analysis a. Mathematical Foundations

Set Theory, Mathematical Logic, Proofs

b. Linear Algebra Vector Spaces, Matrix Algebra, Systems of Linear Equations, Quadratic Forms and Definiteness, Eigenvalues and Eigenvectors, Matrix Decompositions

c. Calculus Topology, Differential Calculus, Integral Calculus

2. Optimization a. Static Optimization

Unconstrained Optimization, Constrained Optimization, Lagrange Method, Kuhn-Tucker Method, Saddle Point Method, Regularity and Sensitivity Analysis, Fixed Point Theorems

b. Dynamic Optimization Dynamic Programming, Bellman's Principle of Optimality, Bellman Equation, Solution Methods, Regularity

3. Stochastic Analysis a. Probability Theory

Probability Foundations, Probability Measure, Random Variable and Distribution, Multivariate Random Variables, (Higher Order) Moments and Integration, Conditioning and Information

b. Statistics Statistics and Random Sampling, Properties of Estimators, Stochastic Processes, Convergence Concepts for Stochastic Processes, Laws of Large Numbers and Central Limit Theorems, Large Sample Properties of Estimators, Classes of Estimators

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Course References:

There are numerous textbooks on the mathematics for economics and finance. No single book is comprehensive. The recommended textbooks on optimization are:

• Dixit, A. K., 1990, Optimization in Economic Theory, 2nd Edition, Oxford University Press.

• Fuente, A. de la, 2000, Mathematical Methods and Models for Economists, Cambridge: Cambridge University Press.

• Simon, C. P. and L. Blume, 1994, Mathematics for Economists, Norton, New York.

• Sundaram, R. K., 1999, A First Course in Optimization Theory, Cambridge University Press.

• (Recommended) Sydsaeter, K. , P. Hammond, A. Seierstad, and A. Strom, 2005, Further Mathematics for Economic Analysis, Prentice Hall.

The recommended textbooks on probability and statistics are:

• Gallant, A. R., 1997, An Introduction to Econometric Theory, Princeton University Press.

• Casella, G. and R. L. Berger, 2001, Statistical Inference, 2nd edition, Brooks Cole.

Further references are available upon request.

Course Rules and Policies:

a) Grades & Evaluation:

• In order to pass the course it is necessary to pass the final exam (grade of 4 or higher). The midterm exam is a bonus that allows you to improve the overall grade by at most .5 points.

• Your grade will be determined based on the following criteria: Final Exam (F), Midterm Exam (M). If you pass the final exam (F≥4), your grade will be computed as follows:

Grade = max(F, .8*F+.2*M)

• In the case of a retake exam, only the grade in the retake exam is retained.

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b) Class Attendance & Participation:

• Class attendance is mandatory. I strongly encourage class participation. Ask if there is something you do not understand!

d) Exams:

• All exams are closed book.

• You must bring a non-programmable calculator and a black or blue ink pen only.

• The final exam covers the entire course.

e) Grading & Regrading:

• You must show all derivations and computations. Numerical results without analytical derivations receive deductions. The solution approach must be clear to the grader.

f) Schedule of Classes:

• The schedule of classes may change and we may spend more or less time on some of the subjects.

Norman Schürhoff Lausanne, 24-Oct-2006

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