Descriptif des cours
Cours introductifs
- A review of probability theory foundations
A review of probability theory foundations
Enseignant responsable :
Volume horaire : 15
Description du contenu de l'enseignement :
Outline : 1. Basics of measure theory and integration 2. Probability : random variables, independence 3. Convergence of random variables 4. Law of Large Numbers and Central Limit Theorem 5. Conditional expectations 6. Martingales in discrete time 7. Gaussian vectors 8. Brownian motion : definition, existence, first properties
Compétences à acquérir :
The aim of this class is to provide a quick review of the probability theory that is required to follow the 1st semester classes in MATH and MASEF. Most of the content should already be familiar to students with a M1 in Mathematics.
UE fondamentales
- Monte Carlo and Finite Differences Methods with Applications to Finance
Monte Carlo and Finite Differences Methods with Applications to Finance
Ects : 6
Enseignant responsable :
Volume horaire : 30
Description du contenu de l'enseignement :
Generalities on Monte-Carlo methods 1. Generalities on the convergence of moment estimators 2. Generators of uniform law 3. Simulation of other laws (rejection method, transformation, …) 4. Low discrepancy sequences
Variance reduction 1. Antithetical control 2. Payoff regularization 3. Control Variable 4. Importance sampling
Process simulation and payoff discretization 1. Black-Scholes model 2. Discretisation of SDEs 3. Diffusion’s bridges and applications to Asian, barrier and lookback options.
Calculation of sensitivities (greeks) 1. Finite differences 2. Greeks in the Black-Scholes model 3. Tangent process and Greeks 4. Malliavin calculus, Greeks, conditional expectations and pricing of American options
Calculation of conditional expectations and valuation of American options. 1. Nested Monte Carlo approach 2. Regression Methods (Tsitsiklis Van Roy, Longstaff Schwartz) 3. Rogers’ Duality
Finite difference methods: the linear case 1. Construction of classical schemes (explicit, implicit, theta-scheme) 2. Conditions for stability and convergence
Finite difference methods: the non-linear case 1. Monotonous schemes: General conditions of stability and convergence 2. Examples of numerical schemes: variational problems, Hamilton-Jacobi-Bellman equations.
Compétences à acquérir :
This course provides an in-depth presentation of the main techniques for the evaluating of options using Monte Carlo techniques.
- Stochastic Calculus
Stochastic Calculus
Ects : 6
Enseignant responsable :
Volume horaire : 48
Description du contenu de l'enseignement :
The course consists of four parts, each occupying roughly 6 hours:
- Preliminaries (Gaussian processes, Brownian motion, martingales, local martingales, variation, quadratic variation)
- Stochastic integration (Isometry extension, Wiener integral, Ito integral, martingale property)
- Stochastic differentiation (Itô processes, Itô's Formula, Girsanov's Theorem)
- Stochastic differential equations (existence and uniqueness, Markov property, generator, connections with PDEs).
Pré-requis recommandés :
Probability theory foundations
Compétences à acquérir :
This course is a practical introduction to the theory of stochastic calculus, with an emphasis on examples and applications rather than abstract subtleties. Click here for more information
Mode de contrôle des connaissances :
Final written exam, in class.
En savoir plus sur le cours :
www.ceremade.dauphine.fr/~salez/stoc.html
Bibliographie-lectures recommandées
- Stochastic Control
Stochastic Control
Ects : 6
Enseignant responsable :
Volume horaire : 24
Description du contenu de l'enseignement :
Relationship between conditional expectations and parabolic linear PDEs. Formulation of standard stochastic control problems: dynamic programming principle. Hamilton-Jacobi-Bellman equation Verification approach Viscosity solutions (definitions, existence, comparison) Application to portfolio management, optimal shutdown and switching problems
Teacher : Bruno BOUCHARD
Compétences à acquérir :
PDEs and stochastic control problems naturally arise in risk control, option pricing, calibration, portfolio management, optimal book liquidation, etc. The aim of this course is to study the associated techniques, in particular to present the notion of viscosity solutions for PDEs.
UE optionnelles (minimum 12 ECTS à valider)
- Computational statistics and Markov chain Monte Carlo methods
Computational statistics and Markov chain Monte Carlo methods
Ects : 6
Enseignant responsable :
Volume horaire : 21
Description du contenu de l'enseignement :
Motivations Monte-Carlo Methods Markov Chain Reminders The Metropolis-Hastings method The Gibbs Sampler Perfect sampling Sequential Monte-Carlo methods
Compétences à acquérir :
This course aims at presenting the basics and recent developments of simulation methods used in statistics and especially in Bayesian statistics. Methods of computation, maximization and high-dimensional integration have indeed become necessary to deal with the complex models envisaged in the user disciplines of statistics, such as econometrics, finance, genetics, ecology or epidemiology (among others!). The main innovation of the last ten years is the introduction of Markovian techniques for the approximation of probability laws (and the corresponding integrals). It thus forms the central part of the course, but we will also deal with particle systems and stochastic optimization methods such as simulated annealing.
- Continuous Optimization
Continuous Optimization
Ects : 6
Enseignant responsable :
Volume horaire : 24
Description du contenu de l'enseignement :
This course will review the mathematical foundations of convex/continuous (iterative) optimization methods. We will focus on the theory and mathematical analysis of a few algorithmic methods and showcases some modern applications of a broad range of optimization techniques. The course will be composed of classical lectures and one numerical session in Python. The first part covers the basic methods of smooth optimization (gradient descent) and convex optimization (optimality condition, constrained optimization, duality) with some general approach (monotone operators) and a focus on convergence rates. We will then address more advanced methods (non-smooth optimization and proximal methods, stochastic gradient descent).
Compétences à acquérir :
The objective of this course is to introduce the students to classical and modern methods for the optimization of (mostly convex) objectives, possibly nonsmooth or high dimensional. These arise in areas such as learning, finance or signal processing.
Mode de contrôle des connaissances :
Examen écrit
Bibliographie-lectures recommandées
Exemples de livres généraux sur l'optimisation (souvent convexe) couvrant des aspects à la fois théoriques (complexité) et pratique (implémentations): Boris Polyak: Introduction to optimization, (1987). J.-B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms (1993). Yurii Nesterov: Introductory lectures on convex optimization, 2004 / Lectures on convex optimization 2018 Jorge Nocedal and Stephen J. Wright: Numerical Optimization, 2006. Dimitri Bertsekas: Convex Optimization Algorithms. Athena Scientific 2015. Amir Beck: First-Order Methods In Optimization, 2019. R. Tyrell Rockafellar: Convex analysis, 1970 (1997). H. Bauschke and P.L. Combettes: Convex analysis and monotone operator theory in Hilbert spaces (Springer 2011) Ivar Ekeland and Roger Temam: Convex analysis and variational problems, 1999. Juan Peypouquet: Convex Optimization in Normed Spaces, 2015
- Derivative products in finance and insurance
Derivative products in finance and insurance
Ects : 6
Enseignant responsable :
Volume horaire : 21
Description du contenu de l'enseignement :
Participants will lear how financial institutions can build and structured products, how they value and hedge them, and what they are done for.
Compétences à acquérir :
The aim of this lecture is to train students in the practical evaluation of derivative products and the control of the associated risks. It also introduces them to the new hybrid structured products that have recently appeared in insurance.
- Game theory, applications in economics and finance
Game theory, applications in economics and finance
Ects : 6
Enseignant responsable :
Volume horaire : 18
Description du contenu de l'enseignement :
A- Basics of game theory: 1. Zero-sum games: value, optimal strategies, saddle points, minmax theorem. 2. N-layers normal form games: equilibria in dominant strategies, Nash equilibria, dominated strategies, Nash’s existence theorem. 3. Extensive form: backward induction, subgame perfection, theorem of Kuhn-Zermelo, behavior strategies and Kuhn’s theorem.
B- Applications: 1. Repeated games and cooperation, folk theorems. 2. Zero-sum repeated games with incomplete information on one side (Aumann-Maschler’s model). Splitting lemma, uniform value. 3. Zero-sum stochastic games: dynamic structure, Shapley operator, theorems of Bewley-Kohlberg and Mertens-Neyman.
Compétences à acquérir :
The first part deals with the basics of game theory, the second one with applications in economics and finance. There will only be time to study 2 of the 3 applications (to be decided).
- Finance haute fréquence : outils probabilistes, modélisation statistique à travers les échelles et problèmes de trading
Finance haute fréquence : outils probabilistes, modélisation statistique à travers les échelles et problèmes de trading
- Machine Learning in finance
Machine Learning in finance
Ects : 6
Enseignant responsable :
Volume horaire : 21
Description du contenu de l'enseignement :
- Introduction to statistical learning: The Vapnik Chervonenkis dimension, PAC learning and the calibration versus prediction paradigm.
- Primal and Dual Problem, Lagrangian and KKT conditions
- Supervised learning: SVM, Mercer’s theorem and the kernel trick, C-SVMs, mu-SVMs, a few words on SVMs for regressions.
- Unsupervised learning: Single class SVMs, clustering, anomaly detection, equivalence of different approaches via duality.
- Introduction to random forests and ensemble methods: bias variance trade-off, bootstrap method
- Remarks on parsimony and penalisation: Ridge and Lasso regressions, dual interpretation of Lasso.
Pré-requis recommandés :
Linear algebra, optimisation, differential calculus
Pré-requis obligatoire :
Linear algebra, optimisation, differential calculus
Compétences à acquérir :
Some Statistical Learning results are presented and applied to credit rating, anomalies detection and yield curves modelling. The principal notions are presented in the context of these case studies in finance.
Mode de contrôle des connaissances :
Final exam
Bibliographie-lectures recommandées
- Term structures: interest rates, commodities and other assets
Term structures: interest rates, commodities and other assets
Ects : 6
Enseignant responsable :
Volume horaire : 21
Description du contenu de l'enseignement :
The term structure is defined as the relationship between the spot price and the futures prices of a derivative instrument, for any delivery date. It provides useful information for hedging, arbitrage, investment and evaluation: it indeed synthesizes the information available in the market and the operators’ expectations concerning the future price of the underlying asset.
In many derivative markets, especially in interest rates and in commodity markets, the concept of term structure is very important, because the contract’s maturity increases as the markets come to fruition. In US 3 months interest rate futures market, for example, the maturities reach 10 years. In this course, the commodity markets are often taken as an example, to help understanding. Extensions to other assets will be done, as often as possible.
Chapter 1 presents a general introduction to derivatives today.
Chapter 2 examines the traditional theories of commodity prices and the explanation of the relationships between spot and futures prices. It proposes an empirical review of the results obtained through these frameworks and explains why these theories are still investigated today. It finally shows how to apply these theories to other assets: exchange rates and interest rates.
The traditional theories are however a bit limited when the whole term structure is considered. As a result, there is a need for a long-term extension of the analysis, which is the very subject of the Chapter 3. We first present a dynamic analysis of the term structure. Then the focus turns towards term structure models. The examples rely on the case commodity prices but can be extended to interest rates. Simulations highlight the influence of the assumptions concerning the stochastic process retained for the state variables and the number of state variables. We then explain the econometric method usually employed for the estimation of the parameters. In the presence of non-observable variables, there is a need for fi ltering techniques. We present the method of the Kalman filters. Finally, we study two main applications, i.e. dynamic hedging and investment valuation.
Chapter 4 is devoted to the study of structural models, ie micro-founded equilibrium models that also examine the interactions between the physical and the derivative markets. In this situation the spot price becomes endogenous. The interactions between prices are studied thanks to rational expectations equilibriums.
Compétences à acquérir :
At the end of this course, the students must have a broad knowledge about the term structures of derivative prices: the theories, the valuation methods, the econometric techniques, the empirical tests as well as the applications.
They will also be trained to use their knowledge on this topic in order to develop a critical view on recent research articles.
This course is optionnal for the MASEF's students.
Mode de contrôle des connaissances :
Ongoing assessment, 20%
Final exam, 80%.
En savoir plus sur le cours :
sites.google.com/site/delphinelautierpageweb/
Bibliographie-lectures recommandées
- Danthine J.P., Donaldson J.B., Intermediate Financial Theory, 2d Ed., Elsevier, 2005.
- Hull J., Options, futures and other derivatives, 15th Ed.
- Kolb R.W. , Overdahl J.A. , Futures, options, and swaps, 5th Ed., Blackwell, 2007.
- Williams J., The economic function of futures markets, Cambridge University Press, 1986
- Wilmott P., Paul Wilmott on Quantitative Finance, 3-volume set, 2nd Ed., Wiley, 2006.
- Valuation of financial assets and arbitrage
Valuation of financial assets and arbitrage
Ects : 6
Enseignant responsable :
Volume horaire : 30
Description du contenu de l'enseignement :
Course outline:
I. Discrete time modelling
I.1. Financial assets
I.2. The No arbitrage condition and martingale measures (FTAP)
I.3. Pricing and hedging of European options; market completeness and 2nd FTAP
I.4. Pricing and hedging of American options (in a complete market)
II. Continuous time modelling
II.1. Financial assets as Itô processes : general theory
II.2. Markovian models : PDE pricing, delta-hedging (European options, barrier options, American options)
II.3. Local volatility models and Dupire's formula
II.4. Stochastic volatility models : how to deal with market incompleteness; (semi-)static hedging; specific models and their properties
Compétences à acquérir :
The lecture starts with discrete time models which can be viewed as a proxy for continuous settings, and for which we present in detail the theory of arbitrage pricing. We then develop on the theory of continuous time models. We start with a general Itô-type framework and then specialize to different situations: Markovian models, local and stochastic volatility models. For each of them, we discuss the valuation and the hedging of different types of options : plain Vanilla and barrier options, American options, options on realized variance, etc. Finally, we present several specific volatility models (Heston, CEV, SABR,...) and discuss their specificities.
Bibliographie-lectures recommandées
Bouchard B. et Chassagneux J.F., Fundamentals and advanced Techniques in derivatives hedging, Springer, 2016. Lamberton D. et B. Lapeyre, Introduction au calcul stochastique appliqué à la finance, Ellipses, Paris, 1999.
UE fondamentales
- Cycle of conferences: strategies and actors of portfolio management
Cycle of conferences: strategies and actors of portfolio management
UE optionnelles (minimum 24 ECTS à valider)
Bloc 1 : Apprentissage pour l'économie et la finance
- Python/Pytorch project
Python/Pytorch project
Ects : 6
Enseignant responsable :
Volume horaire : 15
Description du contenu de l'enseignement :
The Python and PyTorch languages are commonly used to build ML/IA algorithms. The classroom course is complemented by a practical application thesis in economics or finance (e.g. Deep hedging, rapid calculation of expected shortfall, optimal portfolio management, high-frequency trading, solving semi-linear equations of the second order, variance reduction, etc.).
Compétences à acquérir :
- Mastery of Python and PyTorch. Ability to build an ML/IA algorithm.
- Reinforcement learning
Reinforcement learning
Ects : 6
Enseignant responsable :
Volume horaire : 24
Description du contenu de l'enseignement :
Outline:
- Introduction to reinforcement learning (RL) and Markov decision processes (MDP)
- Algorithms for MDPs: dynamic programming, value iteration, policy iteration, linear programming
- Multi armed bandits: exploration vs. exploitation, stochastic bandits, adversarial bandits
- Value-based RL: general ideas and basic algorithms (TD-learning, SARSA, Q-learning)
- Function approximation: linear function approximation, deep neural networks and DQN
- Policy-based and actor-critic RL: policy gradient, natural policy gradient, actor-critic algorithms
- Bandits and RL: regret bounds and UCRL algorithm
- Decentralized MDPs and multi-agent RL: complexity results, simple algorithms (e.g. idependent learners) and their applications (e.g. EV charging, wind farm control)
Organization of lectures in two parts (with 15min break):
- First part: lecture covering main notions
- Second part: more advanced material and/or exercises
Pré-requis obligatoire :
Basic notions in linear algebra and probability theory; Python
Compétences à acquérir :
Reinforcement Learning (RL) refers to scenarios where the learning algorithm operates in closed-loop, simultaneously using past data to adjust its decisions and taking actions that will influence future observations. RL algorithms combine ideas from control, machine learning, statistics, and operations research. A common tread of all RL algorithms is the need to balance exploration (trying knew things) and exploitation (choosing the most successful actions so far). This course will introduce the main models (multi-armed bandits and Markov decision processes) and key ideas for algorithm design (e.g. model-based vs. model-free RL, value based vs. policy based algorithms, on-policy vs. off-policy learning, function approximation).
Mode de contrôle des connaissances :
Homework assignments and project
En savoir plus sur le cours :
https://www.di.ens.fr/~busic/teaching/M2RL/
Bibliographie-lectures recommandées
Books MDPs:
- Martin L. Puterman. Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons. 2014.
- Dimitri P. Bertsekas. Dynamic Programming and Optimal Control, Vol I, 4th Edition, Athena Scientific. 2017.
- Dimitri P. Bertsekas. Dynamic Programming and Optimal Control: Approximate Dynamic Programming , Vol II, 4th Edition, Athena Scientific. 2012.
Books RL:
- Richard S. Sutton and Andrew G. Barto. Reinforcement Learning: An Introduction. Second Edition. MIT Press, Cambridge, MA, 2018.
- Csaba Szepesvari. Algorithms for Reinforcement Learning. Morgan & Claypool Publishers. 2009.
- Sean Meyn. Control Systems and Reinforcement Learning. Cambridge University Press. 2022.
Bandit algorithms:
- Tor Lattimore and Csaba Szepesvari. Bandit algorithms. Cambridge University Press. 2020.
Implementation:
- Gymnasium
- Stable Baselines (reliable implementations of RL algorithms)
- PettingZoo
- SustainGym (A suite of environments designed to test the performance of RL algorithms on realistic sustainability tasks)
Bloc 2 : Finance et gestion des risques
- Contrôle stochastique et marchés de l'énergie
Contrôle stochastique et marchés de l'énergie
Compétences à acquérir :
Energy markets are a natural field of applications for stochastic control modelling framework. Historical applications go from water management to the pricing of swing and demand-side contracts. With the deregulation of electricity and gas markets, new applications have raised the attention of financial economists. In particular, the question of the optimal investment in generation assets in the context of climate change and the questions linked to retail competition. These domains are conducive to the utilization of stochastic differential games. This course is intended to provide a short introduction to the physics of energy market and extensive applications taken for financial and economical research papers. For their evaluation, students are expected to realize a study of a research paper for which they will provide a critical analysis of their understanding of the model, together with the reproduction of the results of the paper.
- Gestion globale des risques : VAR
Gestion globale des risques : VAR
Ects : 6
Enseignant responsable :
Volume horaire : 21
Description du contenu de l'enseignement :
Mesures de risque et régulation (Solvency, Bale): exemple de calculs. Modèles dynamiques pour les prix d ’ actifs financiers. Agrégation des risques de manière très générale, c'est à dire pour différents types de risque sur des exemples, aussi bien en assurance qu'en finance. Risques des produits dérivés également. Modèles multivariés. Implémentation en Python.
Pré-requis obligatoire :
De bonnes bases en théorie des probabilités, en analyse stochastique et en Python.
Compétences à acquérir :
Analyse des modèles mathématiques du risque de marché, étude des méthodes de gestion globales du risque de marché lorsque les sources d ’ incertitude sont multiples.
Mode de contrôle des connaissances :
0.3*CC+0.7*E avec E=examen sur table et CC=contrôle continu.
Bibliographie-lectures recommandées
Ce cous est "self-content" mais ne pas hésiter à combler ses lacunes en lisant un cours de calcul stochastique+EDS et discretisation Euler.
- Microstructure des marchés financiers
Microstructure des marchés financiers
Ects : 6
Volume horaire : 15
Description du contenu de l'enseignement :
The field of market microstructure combines theoretical modeling, institutional knowledge, and empirical analysis to understand how prices result from the interactions of traders in financial markets. The course aims to acquaint students with (i) the canonical models in microstructure, and (ii) econometric models used to test the predictions of microstructure models.
Course structure:
- Trading Mechanisms
- Measuring Liquidity
- Price Dynamics and Liquidity
- Trade Size and Market Depth
- Empirical Analysis
Compétences à acquérir :
Master the concepts of financial markets microstructure
Mode de contrôle des connaissances :
Evaluation: assignment and final exam
Bibliographie-lectures recommandées
Foucault, Thierry, Marco Pagano, and Ailsa Röell, Market Liquidity: Theory, Evidence, and Policy, Oxford University Press, 2013.
- Modélisation stochastique de la courbe de taux
Modélisation stochastique de la courbe de taux
Ects : 6
Enseignant responsable :
Volume horaire : 21
Description du contenu de l'enseignement :
1. Quelques outils de calcul stochastique : rappels 2. Généralités sur les taux d ’ intérêt 3. Produits de taux classiques 4. Modèle LGM à un facteur 5. Modèle BGM (Brace, Gatarek et Musiela) / Jamishidian 6. Modèles à volatilité stochastique
Compétences à acquérir :
Ce cours est consacré aux modèles de taux d ’ intérêts à temps continu. Au travers de nombreux exemples, on décrira leurs utilisations pour évaluer les produits dérivés sur taux d ’ intérêt.
Bloc 3 : Economie et jeux
- Mean field games theory
Mean field games theory
Ects : 6
Enseignant responsable :
Volume horaire : 18
Description du contenu de l'enseignement :
Stochastic Control cours (1rst semester) is a necessary prerequisite.
Mean field games is a new theory developed by Jean-Michel Lasry and Pierre-Louis Lions that is interested in the limit when the number of players tends towards infinity in stochastic differential games. This gives rise to new systems of partial differential equations coupling a Hamilton-Jacobi equation (backward) to a Fokker-Planck equation (forward). We will present in this course some results of existence, uniqueness and the connections with optimal control, mass transport and the notion of partial differential equations on the space of probability measures.
Pré-requis recommandés :
Stochastic analysis, Stochastic control.
Compétences à acquérir :
Mastering of the mean field games technics.
Bibliographie-lectures recommandées
Notes on the course: www.ceremade.dauphine.fr/~cardaliaguet/Enseignement.html
- Variational problems and optimal transport
Variational problems and optimal transport
Ects : 6
Enseignant responsable :
Volume horaire : 24
Description du contenu de l'enseignement :
Chapter 1: Convexity in the calculus of variations
-separation theorems, Legendre transforms, subdifferentiability, -convex duality by a general perturbation argument, special cases (Fenchel-Rockafellar, linear programming, zero sum games, Lagrangian duality) -calculus of variations: the role of convexity, relaxation, Euler-Lagrange equations
Chapter 2: The optimal transport problem of Monge and Kantorovich
-The forrmulations of Monge and Kantorovich, examples and special cases (dimension one, the assignment problem, Birkhoff theorem), Kantorovich as a relaxation of Monge -Kantorovich duality -Twisted costs, existence of Monge solutions, Brenier ’ s theorem, Monge-Ampère equation, OT proof of the isoperimetric inequality -the distance cost case and its connection with minimal flows
Chapter 3: Dynamic optimal transport, Wasserstein spaces, gradient flows
-Wasserstein spaces -Benamou-Brenier formula and geodesics, displacement convexity -gradient flows, a starter: the Fokker-Planck equation, general theory for lambda-convex functionals
Chapter 4: Computational OT and applications
-Entropic OT, Sinkhorn algorithm and its convergence -Matching problems, barycenters, -Wasserstein distances as a loss, Wasserstein GANs
Compétences à acquérir :
Mastering of variational and optimal transport methods used in economy.
Projet individuel
- Mémoire de fin d'études
Mémoire de fin d'études
Formation année universitaire 2025 - 2026 - sous réserve de modification
Modalités pédagogiques
Les Modalités des Contrôles de Connaissances (MCC) détaillées sont communiquées en début d'année.
Les enseignements de la deuxième année de Master mention Mathématiques et Applications pour le parcours Mathématiques de l’Assurance, de l'Économie et de la Finance (MASEF) sont organisés en semestres 3 et 4.
Le semestre 3 est constitué d’UE fondamentales et d'UE optionnelles et le semestre 4 est constitué d'une UE fondamentale et d'UE optionnelles parmi trois blocs thématiques :
- Apprentissage pour l'économie et la finance
- Finance et gestion des risques
- Économie et jeux
auquel s’ajoute une UE de stage.
La formation démarre en septembre, la présence en cours est obligatoire. Certains cours ont lieu à l’ENS ou à Sorbonne Université.
Stages et projets tutorés
Les étudiants doivent effectuer un travail de recherche complémentaire donnant lieu à la rédaction d’un mémoire de fin d'étude individuel. Ce travail de recherche peut éventuellement être remplacé par un stage en entreprise d’une durée minimum quatre mois, suivi de la rédaction d'un mémoire portant sur le sujet du stage. Une soutenance est organisée. La note du stage est attribuée après la soutenance et
conditionne l'obtention de 4 ECTS.
Ce stage doit alors être de nature technique afin d’être validé par le responsable du parcours MASEF.
L'étudiant est chargé de trouver son stage par ses propres moyens.
Des programmes nourris par la recherche
Les formations sont construites au contact des programmes de recherche de niveau international de Dauphine, qui leur assure exigence et innovation.
La recherche est organisée autour de 6 disciplines toutes centrées sur les sciences des organisations et de la décision.
En savoir plus sur la recherche à Dauphine