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Mathematics for Economics and Finance

  • Enseignant(s): N.Schuerhoff
  • Titre en français: Mathématiques pour l'Economie et la Finance
  • Cours donné en: anglais
  • Crédits ECTS: 6 crédits
  • Horaire: Semestre d'automne 2013-2014, 2.0h. de cours + 2.0h. d'exercices (moyenne hebdomadaire)
  •  séances
  • site web du cours site web du cours
  • Formations concernées:
    Maîtrise universitaire ès Sciences en économie politique

    Maîtrise universitaire ès Sciences en finance

Objectifs

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.

Contenus

Part I.          Real Analysis

a.    Mathematical Foundations

Set Theory, Mathematical Logic, Proof Theory

b.    Linear Algebra

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

c.    Calculus

Topology, Differential Calculus, Integral Calculus

Part II.       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

Part III.    Optimization

a.    Static Optimization

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

b.    Dynamic Optimization

Fixed-Point Theorems, Contractions, Bellman's Principle of Optimality, Bellman Equation, Dynamic Programming, Solution Methods, Regularity

Références

Detailed lecture notes will be provided. There are numerous textbooks on the mathematics for economics and finance. A number of recommended textbooks will be provided in class. Further references are available upon request.

Evaluation


 

1ère tentative


 
Examen:
Ecrit 3h00 heures
Documentation:
Non autorisée
Calculatrice:
Autorisée avec restrictions
Evaluation:

Normal : écrit, 3heures, doc non autorisée, calculatrice basique autorisée


 

Rattrapage


 
Examen:
Ecrit 3h00 heures
Documentation:
Non autorisée
Calculatrice:
Autorisée avec restrictions
Evaluation:

Rattrapage : écrit, 3heures, doc non autorisée, calculatrice basique autorisée



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