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. Fixed Point Theorems
One-dimensional Problem (R1), Multi-dimensional Problem (Rn), Contractions
c. Dynamic Optimization
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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