Dynamic Optimization
 /  Dynamic Optimization
Dynamic Optimization

Professor: : Naila Hayek, Professeur des Universités en Mathématiques Appliquées à l’Université Paris II.

Objective: The aim of this course is to provide some useful mathematical models and tools in economics and finance. The first part of the course is devoted to reminders of static optimization: optimization without constraints and under equality and inequality constraints, to which are added depths and applications. The second part of the course focuses on the dynamic optimization: Calculus of Variations and Optimal Control.

Outline:

I – Static optimization

1/ Optimization without constraint and under constraints

- The Lagrange multipliers; the Kuhn and Tucker theorem

2/ The generalized Lagrangian

3/ Applications: portfolio management , hedging on a futures market

 

II - Dynamic Optimization

1/ Calculus of Variations

- Necessary conditions and sufficient conditions of optimality; Euler-Lagrange Equation

- Applications: consumption-saving problem, ...

2/ Deterministic Optimal Control

- Necessary conditions and sufficient conditions of optimality; the Pontryagin Maximum Principle

- Applications: portfolio management in the presence of transaction costs, ...

3/ Introduction of Dynamic Programming

 

Grading: Final exam at the end of the semester.

Bibliography:

  • Demange G & Rochet J.C. Méthodes mathématiques de la finance. 3e edition Economica. 2005 ;
  • Hayek N. & Leca J.P. Mathématiques pour l’Economie. Analyse-Algèbre. 5e edition Dunod. 2015.

 


Speakers
  • Naila HAYEK
    Professeur de mathématiques appliquées à l’Université Paris II Panthéon-Assas. Co-directrice du Magistère Banque-Finance et du Master II Techniques Financières et Bancaires.

General information

Address :

122, rue de Vaugirard
75006 Paris, FRANCE

L4 L6 L12 L13 Montparnasse
L10 L13 Duroc
L4 Saint-Placide
L12 Falguière

Phone :
+33 (0)1 53 63 80 76

Email :
secretairembf@u-paris2.fr

RECRUITMENT

Shortlisted results announced
15 juin 2021

Interviews
24 et 25 juin 2021

Final admission results
1er juillet 2021

Administrative registration
Du 1er au 15 juillet 2021

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