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MICROECONOMICS 1 Course Syllabus

First Semester 2006-2007—Paris Course Title Microeconomics 1 Instructors Dr. J.M. Bonnisseau and Dr. J.Ph. Médecin E-mail [email protected] and [email protected] Course Objective This course is the first one in a sequence of three courses that aim to cover

Microeconomics at the Graduate level. Each course can be taken independently. Even if no prerequisite is asked in microeconomics, a course of Intermediate Economics may help. This course is dedicated to study the behavior of consumers and producers in a perfect competition framework.

Required Texts and References

Mas-Colell, A., Whinston, M.D., Green, J., Microeconomic Theory, Oxford University Press, 1995. Chapters 1-5, 10 and 15-18.

Description Behavior of consumers and producers, theory of demand and supply, existence

theorem, welfare theorems Course Content

- Consumer preferences and utility representation - Competitive demand, properties and computation on some examples - Indirect utility function, expenditure function and compensated demand, definition and relationships among them - Differential characterization of the demand for differentiable utility function - Production set, production function, cost function - Efficiency - Aggregation of production sets - Competitive behavior, profit function, supply function - Cost minimization and profit maximization - Edgeworth box - Aggregate excess demand function - Existence of general equilibrium - First and second welfare theorems

Teaching Method Lecture, discussion and problem solving Oral & Written Communications Content Discussion in class and problem solving on exams Attendance Mandatory. You are responsible for all the material covered in class as well as all

announcements, whether you are present or not. Evaluation Two in-class exams plus a mid-term exam and a final exam. Each exam counts

for 20% of the students' final grade. The last 20% are provided by the participation.

Each in-class exam date will be announced in class two weeks prior to the exam. The mid-term exam will be given on the date announced on the web site. The final

exam is scheduled in the week of December 11, 2006. Results The grades will be sent to QEM office on Monday, 8th of January.


First Semester 2006-2007—Bielefeld Course Title Microeconomics 1 Instructors Prof.Dr.Walter Trockel, Room W 10-108 Office hours: Wendesday 11:00 – 13:00,

Tutorials : Christian Hermelingmeier (Dipl.Wirt.-Math.,Doctoral Student of EBIM) Room V8 - 235 Special office hours for tutoring

E-mail [email protected] Course Objective Required Texts and References

Mas-Colell, A., Whinston, M.D., Green, J., Microeconomic Theory, Oxford University Press, 1995. Chapters 1-6,10,15-17.

Description Microeconomic Theory by Mas-Colell ,Whinston & Green (MWG), Chapters 1-

6,10,15-17 Course Content

Exercises (all in the book of MWG ;the superscript B in the book just says that it is at this stage of medium difficulty, A would be easy, C would be difficult). 1.B.3,1.B.5,1.C.1,1.D.1,1.D.3 ( you should be able to solve these in less than 30 minutes). 2.E.5,2.E.7,2.F.4,2.F.14,2.F.16 ( 3.C.4,3.C.5,3.C.6 2.F.17,3.F.2,3.F.1,3.I.5,( Try: 3.J.1. hard!! )( ca. 30 min without 3.J.1 ) 4.C.11,4.C.12,4.D.5,( ca 60 to 80 min) 6.B.3,6.B.4,6.C.4,6.C.14 ( ca 60 to 90 min ) 15: B.1, B.2, B.3, B.6,C.1,D.3,D.5 16: C.2,D.1,D.2, D.3,E.2, AA.2,AA.3

Advice Cooperate in groups!! Try to understand the basic concepts and why they are mathematically formalized as they are! If you worked hard and did not succeed consult the solution manual! After that, if still things are unclear, go to an office hour of Christian and ask for help. Notice:The predominant B -type of exercises in MWG is representative for the level of difficulty in the final exam.

Teaching Method Oral & Written Communications Content Attendance Evaluation

MACROECONOMICS 1 Course Syllabus

First Semester 2006-2007—Paris Course Title Macroeconomics I Instructors Dr. Bertrand Wigniolle E-mail [email protected] Course Objective This course is the first one in a sequence of three courses that aim to cover

Macroeconomics at the Graduate level. This first course is a prerequisite to follow macroeconomics II and/or III. An introductory part presents the basic notions and concepts used in macroeconomics. A first part is devoted to real macroeconomics: long run growth, consumption behaviour and labour market. A second part is devoted to short run macroeconomics: dynamics of inflation and unemployment, macroeconomic policy in an open economy.


David Romer, Advanced macroeconomics, (Mac Graw-Hill, second edition, 2001). Students who have never studied macroeconomics could use the following textbook as an introduction: O. Blanchard, Macroeconomics, (Prentice Hall, 4th Edition, 2005).

Description Economic Growth, Consumption behaviour, the labor market, the dynamics of

inflation and unemployment, macroeconomic policy in an open economy. Course Content - Introduction of the main concepts and notions in macroeconomics

- Empirical evidence on growth - The Solow model - Analysis of convergence - The life cycle model of consumption - Some empirical facts on the labor market - The bargaining theory - Efficiency wages - Matching models - The Phillips’ curve and the dynamics of inflation and unemployment - Rational expectations and macroeconomic policy - Rules versus discretion - Credibility and delegation - The Mundell-Fleming model



for 20% of the students' final grade. The last 20% are provided by the participation. Each in-class exam date will be announced in class two weeks prior to the exam. The mid-term and final exams will be given on the date announced on the web site.


First Semester 2006-2007—Bielefeld Course Title Macroeconomics 1 Instructors Dr. Thorsten Pampel E-mail [email protected] Required Texts and References

Böhm/Wenzelburger: Lecture notes on the theory of economic growth De la Croix/Michel: Dynamics and policy in Overlapping Generations

Course Content

1. Aggregate Models of Economic Growth 1.1 The basic model with exogenous savings 1.2 Existence of balanced growth paths 1.3 Stability of balanced growth paths 1.4 Examples with different technologies 2. Wealth, Factor Shares, and Cycles 2.1 The Kaldor growth model 2.2 Dynamics and bifurcations 2.3 The Pasinnetti growth model 3. Different extensions (an overview) 3.1 Growth with Random Perturbations 3.2 Exogenous technological progress 3.3 Endogenous growth: The AK model 4. Optimal Economic Growth 4.1 The golden rule of capital accumulation 4.2 The Ramsey problem 4.3 Dynamics of optimal growth 5. Economic Growth with Overlapping Generations 5.1 Durable commodities and storage 5.2 The role of expectations 5.3 Dynamics with perfect foresight 5.4 Intertemporal allocations and welfare 5.5 Stationary equilibria and Pareto optimality 5.6. Capital Accumulation and overlapping generations 6. Fiscal Policy in OLG Models 6.1 Unfunded pension systems 6.2 Pareto improving pension system with over accumulation 6.3 Government debt and wealth with balanced budgets 6.4 Government consumption and permanent deficits

Teaching Method The course has stimulated several questions and the combination of the lecture

and the exercises allowed the students to refind results from the lecture by their own in the exercises as well as in the exams.

Evaluation midterm exam (Take home); final exam (take home + class exercise)

FINANCIAL ECONOMICS Course Syllabus

First Semester 2006-2007—Paris Course Title Financial Economics Instructors Dr. Etienne Koehler E-mail [email protected] Course Objective Required Texts and References

Rajna Gibson: “Obligations and clauses optionnelles”; ed: PUF Pierre Chabardès and François Delclaux: »Les produits dérivés » ;ed: Gualino Frank and Dessa Fabozzi: « The handbook of fixed income securities 4th edition »; ed: Irwin John Hull: “Options, Futures and other derivatives (5th edition)” ; Prentice Hall Chazot & P. Claude: “Les Swaps”; ed: Economica

Description Course Content

I. Some words on the interest rates building up A. Time or market transfers B. Opportunity cost C. Default risk D. Inflation risk E. Interest rates and maturity

1. The risk increases with time 2. Segmentation vis-a-vis the duration 3. Links between rates

F. References II. Future and Present Value

A. Future Value 1. Simple interests (ex: Euribor is in Bond basis) 2. Compounded rates

a) Annual rates b) Semi annual or monthly rates

3. Continuous rates 4. Examples of future value computations

a) Euribor b) Compounded rates

B. Present Value = reciprocal of Future Value 1. Definitions 2. Examples of Present Value computations 3. DFs

a) Annual rates b) Semi annual or monthly rates c) Continuous rates

4. Particular investments discounting a) Multiple Cash-flows b) Annuities

III. Bonds and swaps A. Fixed coupon bonds

1. Definition, accrued interest

2. Return definition a) Current yield b) Actuarial yield

3. Zero-coupon bonds a) Yields and rates b) Bonds and ZC portfolio

4. Par, premium and discount 5. Forward ZCs and forward ZC rates 6. Instantaneous forward rates 7. Examples: BTF, BTAN, OAT

B. Swap rate 1. IBM example 2. Receiver or payer swaps 3. Pricing of a receiver swap

IV. Duration and convexity A. Duration

1. Risk of rate a) Initial level of rates b) Yield level c) Direction of yield variation d) Rate of coupon e) Bond maturity

2. Duration a) Definition b) Properties

B. Convexity 1. Bond convexity definition 2. Properties of the bond convexity

C. Swaps CMS V. Zero coupon curve

A. Practical example. B. From swaps to ZC

VI. Options A. Options on Equity B. Caps/Floors; swaptions


announcements, whether you are present or not. Evaluation A mid-term exam and a final exam. Each exam counts for 40% of the students'

final grade. The last 20% are provided by the participation. The mid-term exam will be given on the date announced on the web site. The final exam is scheduled in the week of December 11, 2006.

FINANCIAL ECONOMICS Course Syllabus

First Semester 2006-2007—Bielefeld Course Title Financial Economics Instructors Dr. Frank Riedel, Tutorial: Jan-Henrik Steg E-mail [email protected], [email protected] Course Objective Required Texts and References

LeRoy, Werner, principles of Financial Economics, Cochrane, Asset Pricing Riedel, Lecture Notes

Description The course is divided into two sections : International Finance and Portfolio

Management. In the International Finance section, students will study the international financial market as a whole, and not as an amalgamation of various national markets. The second section looks at modern Portfolio Management, including current theory, asset pricing models, and asset allocation, management strategies, and performance.

Course Content

Basics of General Equilibrium Theory for Financial Economics Equilibrium Theory of Financial Markets: Complete and Incomplete Markets No—Arbitrage Theory: Fundamental Theorem of Asset Pricing I and II Option Pricing Multiperiod Models Information and Martingales Extension of the Basic Theorems to the Multiperiod Model American Options Consumption—Based Capital Asset Pricing Outlook: Continuous—Time Models, Black—Scholes

Teaching Method Oral & Written Communications Content Attendance Evaluation

INTERMEDIATE PROBABILITY Course Syllabus

First Semester 2006-2007—Paris Course Title Intermediate Probability Instructors Dr. M Meddeb and Dr. C. Chorro E-mail [email protected] and [email protected] Course Objective The objective of this course is for the students to develop an understanding of the

basic concepts of probability theory. We limit ourselves to the finite case in order to overcome technical aspects.

Required Texts

The main text is LIPSCHUTZ and LIPSON, Schaum’s Outline of Probability. The course will also use material from JACOD, J. and PROTTER, P., Probability Essentials, Springer, second printing 2004, pages 1 to 50, which is the recommended book for Probability.

Description Combinatory, probability in finite case Course Content

- Set theory - Combinatory -Axioms of probability - Conditional probability - Random variables in the finite case, expectation - Classical examples (Bernoulli, Binomial, etc...) - Independance

Teaching Method Lecture (2h30 per week), discussion and problem solving (2h30 per week) Attendance Mandatory. You are responsible for all the material covered in class as well as all


final grade. The last 20% are provided by the participation. Each in-class exam date will be announced in class two weeks prior to the exam. The mid-term exam will be given on the date announced on the web site. The final

exam is scheduled in the week of October 23, 2006. Results The grades will be sent to QEM office on Monday, 8th of January.

PROBABILITY THEORY Course Syllabus

First Semester 2006-2007—Paris Course Title Probability Theory Instructors Dr. M Meddeb and Dr. C. Chorro E-mail [email protected] and [email protected] Course Objective This course introduces the student to the fundamentals of rigorous probability

theory. The intention of this course would be to prepare the student to go on to advanced probability-related topics such as Brownian motion and Ito calculus.

Required Texts

JACOD, J. and PROTTER, P., Probability Essentials, Springer, second printing 2004.

Description Discrete and continuous random variables, convergence of sequences of random

variables, conditional expectation Course Content

- Sigma-algebra, axioms of probability - Integration with respect to a probability measure - General random variables (continuous and discrete cases) - Classical examples (Poisson, exponantial, Gaussian, etc....) - Expectation, Markov and Tchebycev inequalities - Independance of random variables - Law of large numbers - The central limit theorem and its applications - L^2 and Hilbert spaces - Conditional expectation - Martingales

Teaching Method Lecture (2h30 per week), discussion and problem solving (2h30 per week) Attendance Mandatory. You are responsible for all the material covered in class as well as all

announcements, whether you are present or not. Evaluation A final exam that counts for 80% of the students' final grade. The last 20% are

provided by the participation. The final exam is scheduled in the week of December 11, 2006.

Results The grades will be sent to QEM office on Monday, 8th of January.

PROBABILITY THEORY Course Syllabus

First Semester 2006-2007—Bielefeld Course Title Probability Theory Instructors Dr. H. Mashurian E-mail Course Objective Required Texts and References


Elementary set theory Elementary combinatorics Probability Conditional probability Independence Random variables Expectation, variance and higher moments Basic distributions The Poisson process Construction of probability measures Integration Sums of independent random variables Convergence types for random variables Laws of large numbers Central limit theorem

Teaching Method Oral & Written Communications Content Attendance EVALUATION

INTERMEDIATE OPTIMIZATION Course Syllabus

First Semester 2006-2007—Paris Course Title Intermediate Optimization Instructors Pascal Gourdel E-mail [email protected] Course Objective The aim of this course is to present the general basis of Optimization Theory. It

started to present an elementary theory of convex sets and functions. The particular case of dimension 1 is treated cautiously in order to introduce the difficulties (necessary conditions, sufficient conditions, characterization of convex functions, qualification condition...)

Finally the theorem of Karush-Kuhn-Tucker is stated without proof. Economic applications of this theorem are given and also Farkas' lemma.


Simon, C., Blume, L., Mathematics for Economists, (1994) Norton. De La Fuente, A., Mathematical Methods and Models for Economists, 2nd Ed. (2005) Cambridge University Press.

Description Convexity and Optimization Course Content

1. Convexity of sets and functions. 1.1 Convex sets. Examples : budget sets, balls, production sets. 1.2 Convex and concave functions, graph, epigraph and hypograph. 1.3 Quasiconvex and quasiconcave functions. 1.4 Strictly convex and quasi convex functions. 1.5 Characterization of a convex funtion with its first order derivative 1.6 Characterization of a convex funtion with its second order derivative. 2. Optimization under constraints 2.1. Unconstrained optimization. 2.1.1. Global and local maximum (minimum). 2.1.2. First order necessary conditions. 2.1.3. Second order necessary condition and second order sufficient condition. 2.1.4. Global maxima for concave (convex) functions. Examples. 2.2. Constrained optimization. 2.2.1. Convexity conditions and Slater condition. 2.2.2. The Kuhn-Tucker problem in convex programming (statement without proof) 2.2.3. Applications of Kuhn-Tucker Theorem in consumer theory and producer theory 2.2.4. More examples of Applications of Kuhn-Tucker Theorem


announcements, whether you are present or not.

Evaluation Two in-class exams plus a mid-term exam and a final exam. Each exam counts



exam was of December 12, 2006. for Intermediate Optimization Results The grades were sent to QEM office on Sunday, 7th of January.

OPTIMIZATION Course Syllabus

First Semester 2006-2007—Paris Course Title Optimization Instructors Pascal Gourdel E-mail [email protected] Course Objective The aim of this course is to present the general basis of Optimization Theory. It

started to present an elementary theory of convex sets and functions. In addition to the program of Intermediate Optimization, we study here the notions of polarity, normal and tangent cones (convex case) in order to proof completely the theorem of Karush-Kuhn-Tucker (convex case).


Simon, C., Blume, L., Mathematics for Economists, (1994) Norton. De La Fuente, A., Mathematical Methods and Models for Economists, 2nd Ed. (2005) Cambridge University Press.

Description Convexity and Optimization Course Content

1. Complements on convexity Topological properties of convex sets. Projection on a closed convex set. Separation theorems. Orthogonality and polarity. The bipolar theorem. Farkas lemma. 2. Complements on optimization Proof of the Kuhn-Tucker theorem in convex programming. Linear programming Duality theory in linear programming and convex programming





exam was given on the week of December 11, 2006. Results The grades were sent to QEM office on Sunday, 7th of January.

OPTIMIZATION Course Syllabus

First Semester 2006-2007—Bielefeld Course Title Optimization Instructors Dr. Benteng Zou E-mail Presentation The aim of this course is to present and deepen various of mathematical

concepts, problem formulation, analytical methods for optimization. This serves as an introduction to a wide variety of optimization problems and techniques including convex analysis, unstrained optima, equality constraints and inequality constraints, Kuhn and Tucker theorem, Pontryagin maximum principle, and dynamic programming.


1. Sundaram R. K., A first course in Optimization Theory, Cambridge Univ. Press, 1996. 2. Evans, L. C., An introduction to mathematical optimal control theory, online version. 3. Florenzano and le Van, Finite dimensional convexity and optimization, Springer, 2001. 4. Dixit, Optimization in Economic theory, second edition, Oxford Univ. Press, 1990.

Course Objectives To define and illustrate the terms used in the study of optimization theory, such

as convex analysis, Kuhn and Tucker theory, maximum principle, dynamic programming, and Hamiltonian-Jacobin- Bellman equation.

To demonstrate and apply techniques of optimization theory and application in economics. Different economic models will be explained from mathematics point of view.

To formulates and solve optimal control problem via Pontryagin’s necessary conditions, Kuhn and Tucker theorem, and dynamic programming.

Course Content

-Introduction and notation -Unconstraint Optima (Chapter 4 of Sundaram ) -Equality constraints and the theorem of Langrage (Chapter 5 of Sundaram ) -Inequality constraints and the theorem of Kuhn and Tucker (Chapter 6 of Sundaram) -Convex structure in Optimization theory (Chapter 7 of Sundaram, or Chapter 7 of Florenzano and le Van) -Quasi-convexity and optimization (Chapter 8 of Sundaram, or Chapter 8 of Florenzano and le Van) -Parametric continuity: The Maximum theorem (Chapter 9 of Sundaram) -The Pontryagin maximum principle (Chapter 4 of Evans) -Dynamic programming (Chapter 10 and 11 of Dixit)

Requirements There will be several homework set (Collaboration on homework is encouraged,

but NOT in exam), registered students must write up and hand in their solutions individually. There will be one final writing exam (2 hours).

Evaluation Homework 25%+Final exam 75%. Homework is not acceptable one week later

than the deadline.

Reading List 1. Kamien and Schwartz, Dynamic otimization, the calculation of variations and optimal control in economics and management, second edition.

2. Ekeland and Turnbull, Infinite-dimesional optimization and convexity, The University of Chicago Press, 1983.

3. Varaiya, Lecture notes on optimization, online. 4. Boyd and Vandenberghe, Convex optimization, Cambridge univ. Press, 2004(also online).

5. BARBU, LECTURES ON OPTIMAL CONTROL OF DIFFERENTIAL SYSTEM, ONLINE.


Second Semester 2006-2007—Paris Course Title Microeconomics 2 Instructors Dr. J.Abdou and Dr. J.M. Tallon Email mailto:[email protected], mailto:[email protected] Course Objective This course is composed of two parts. The first is dedicated to an introduction of

Game Theory while the second is concerned by information problems in economic contexts

Texts and References Part I Mas-Colell, A., Whinston, M.D., Green, J., Microeconomic Theory, Oxford University Press, 1995. Chapters 7-9 M.J. Osborne and A. Rubinstein, A course in Game Theory, The MIT Press, 1994 Chapters 1-7 and 11.

Part II The main text for the course will be Contract Theory, by P. Bolton and M.

Dewatripont, MIT Press 2005 Other relevant textbooks: Incentives, by D. Campbell, Cambridge University Press, 1995 The Theory of Incentives, by J.J. Laffont and D. Martimort, Princeton University

Press, 2002 An Introduction to the Economics of Information I. Macho-Stadler and D. Perez-

Castrillo, Oxford University Press, 1997 Microeconomic Theory, A. Mas-Colell, M. Whinston and J. Green, Oxford

University Press, 1995 The Economics of Contract: a Primer, by B. Salanié, 2nd edition, MIT Press, 2005 The Theory of Corporate Finance, by J. Tirole, Princeton University Press, 2006 Description Part I Strategic behavior of rational agents in interactions with conflictual interests

Part II Economics of Information, or more specifically, what is known as Incentive Theory or Contract Theory

Course Content Part I, Strategic form and dominance concepts Nash Equilibrium Zero-Sum games , value, optimal strategies Perfect information extensive form Mixed strategies General Information extensive form

Part II 1 Introduction: Optimal contracts under uncertainty; information and incentives; 2. Hidden information, screening 3. Hidden information, signalling 4. Hidden action, moral hazard 5. Disclosure of private certifiable information 6. Multilateral asymmetric information: bilateral trading and auctions

7. Incomplete contracts and institution design 8. Foundations of contracting with unverifiable information 9. Markets and contracts


announcements, whether you are present or not. Evaluation An exam on Part I and an Exam on Part II. Each exam counts for 40% of the

students' final grade. The last 20% are provided by the participation.


Second Semester 2006-2007—Paris Course Title Advanced Macroeconomics Instructors Antoine d’Autume and Thomas Seegmuller E-mail [email protected] and [email protected] Course Objective This course is the second one in a sequence of courses that aim to cover

macroeconomics at the Graduate level. This course is dedicated to short term macroeconomics : the determination of production and employment in an open economy ; business cycles and stabilization policies. Macro 3 is dedicated to long run macroeconomics. Macro 2 and 3 are obviously complementary, but may be chosen independently. Macroeconomics 1 is a prerequisite for both.


Romer, D (2005): Advanced Macroeconomics. New-York: Mc Graw-Hill. Third Edition.

Blanchard, O. et S. Fisher (1989): Lectures on Macroeconomics. Cambridge: MIT Press.

Blanchard O. J. (2005): Macroeconomics. Prentice Hall. Fourth Edition. Description Open macroeconomics, the dynamics of inflation and unemployment, the

neoclassical synthesis, new Keynesian economics, imperfect competition in macroeconomics.

Course Content

- aggregate demand and supply - open macroeconomics - exchange rates and the balance of payments - the dynamics of inflation and unemployment - stabilization policies - static models with imperfectly competitive product market - market power on product and labor markets, and underemployment - fiscal policy and public spendings under imperfect competition - monetary policy, neutrality and nominal rigidities - coordination failures - some macro-dynamic implications of imperfect competition




Each in-class exam date will be announced in class two weeks prior to the exam. The mid-term and final exams will be given on the date announced on the web

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Course Outline

Macroeconomic Theory SS 2007

Beleg-Nr. 315204 – SS 07

Version: 16th January 2007

Contents

1 Introduction 2

2 Microeconomic Foundations 2

2.1 Intertemporal Decisions of Consumers . . . . . . . . . . . . . . . . . . . . . . 2

2.2 Intertemporal Decisions of Producers . . . . . . . . . . . . . . . . . . . . . . 2

2.3 Theory of temporary Walras Equilibria . . . . . . . . . . . . . . . . . . . . . 2

3 Theory of Non Walrasian Temporary Equilibria 3

4 Monetary Equilibrium Models 3

4.1 Temporary Competitive Equilibrium in the Macroeconomy . . . . . . . . . . 3

4.2 Noncompetitive Wage Models . . . . . . . . . . . . . . . . . . . . . . . . . . 3

5 Dynamics of Monetary Equilibrium Models 3

5.1 Dynamics of Expectations, Prices, and Money Balances . . . . . . . . . . . . 3

5.2 Dynamics wit Random Perturbations . . . . . . . . . . . . . . . . . . . . . . 3

6 The Keynesian Model with Money: Prices, Wages, and Employment 3

6.1 Disequilibrium Price and Wage Adjustment . . . . . . . . . . . . . . . . . . 3

6.2 Steady States and Long Run trade o!s . . . . . . . . . . . . . . . . . . . . . 3

6.3 Stability, endogenous cycles, and complexity . . . . . . . . . . . . . . . . . . 3

6.4 Business cycles with random perturbations . . . . . . . . . . . . . . . . . . . 3

7 Government Bonds and Asset Markets 3

8 Inventory, Capital, and Growth 3

REFERENCES 4

References

Azariadis, C. (1993): Intertemporal Macroeconomics. Blackwell Publishers, Oxford a.o.

Blanchard, O. J. & S. Fischer (1989): Lectures on Macroeconomics. MIT Press, Cam-bridge (Mass.) a.o.

Bohm, V. (1980): Preise, Lohne und Beschaftigung. J.C.B. Mohr (Paul Siebeck), Tubingen.

(1989): Disequilibrium and Macroeconomics. Blackwell Publishers, Oxford a.o.

Dornbusch, R. & S. Fischer (1991): Lecture on Macroeconomics. MIT Press, Cambridge(Mass.) a.o.

Felderer, B. & S. Homburg (1987): Macroeconomics and New Macroeconomics.Springer-Verlag, Berlin a.o.

Grandmont, J.-M. (1983): Money and Value – A Reconsideration of Classical and Neo-classical Theories. Cambridge University Press, Cambridge (Mass.) a.o.

Patinkin, D. (1965): Money, Interest and Prices. Harper & Row, New York.

4

PROBABILISTIC METHODS FOR FINANCE Course Syllabus

Second Semester 2006-2007—Paris Course Title Probabilistic Methods for Finance Instructors Dr. P. Bich E-mail [email protected] Course Objective This course is an introduction to the subject of financial derivatives (futures,

forward, call, put) in a random area; probabilistic tools will be used. Prerequisite: a basic course on probability (but I will remind rapidly what must be known).


John Hull: Options, futures and other derivatives (prentice hall); Wilmott: "Paul Wilmott on quantitative finance", only the first chapters.

Description Derivatives, binomial model, Model for stock prices, Black and Sholes model. Course Content

0) Mathematical prerequisites. probability, sigma-algebra, random variables, mean, expectation, normal law, central limit theorem, conditionnel expectation, radon-nykodym. 1) Introduction. a) Present value, discretely interest, compound interest,... b) Stocks, commodities, currencies, indices. c) Derivatives: forward, futures, ... d) Options: calls, puts, binary, bull spreads, straddles, butterflies ... 2) Forward and Futures. 3) Options markets. a) Generalities b) Introduction to binomial model: cox-ross-rubinstein. 3) Model for stock prices: continuous time models. a) Introduction. b) Markov property. c) Martingale property. d) Quadratic variation. e) Brownian motion and ito process. f) stochastic integration. g) ito lemma. h) first applications. 4) Black and Scholes model. a) delta hedging. b) no arbitrage. c) Black-scholes Equation. d) Girsanov

Teaching Method Lecture, discussion and problem solving

Oral & Written Communications Content Discussion in class and problem solving on exams Attendance Mandatory. You are responsible for all the material covered in class as well as all


final grade. The last 20% are provided by the participation. The dates for the exams will be announced on the website.

FINANCIAL ECONOMICS 2 Course Syllabus

Second Semester 2007—Bielefeld Course Title Financial Economics II Instructors Prof. Frank Riedel E-mail [email protected] Course Objective The course offers an introduction to the main results and models in

continuous--time finance. After a thorough introduction in stochastic calculus, we treat the essential theory of no arbitrage pricing, including the First and Second Fundamental Theorem of Asset Pricing. On this basis, we study hedging and pricing of European and American options in complete and incomplete markets. We move on to characterize optimal portfolios for various types of utility functions. Finally, we sketch new developments in equilibrium theory, credit risk, irreversible investment, and risk measures.

Required Texts and References Björk, Arbitrage Theory in Continuous Time Duffie, Dynamic Asset Pricing Theory Description Theory of Financial Markets in Continuous Time Course Content - Introduction to Main Questions in Continuous--Time Finance

- Brownian Motion - The Main Mathematical Tools for Finance: Itô--Calculus, Girsanov Transformation, Martingale Representation - The Asset Market Model: Self--Financing Strategies and Budget Constraints - No Arbitrage Theory: Fundamental Theorem of Asset Pricing I and II - Pricing of European Options: Black--Scholes--Theorem, - American Options - A Digression on Optimal Stopping\\ - Real Options and Irreversible Investment - Optimal Portfolios and Equilibrium Theory:\\ - Merton's Model, Other Utility Functions - Interest Rates and Credit Risk, Risk Measures

Teaching Method Lecture, discussion and problem solving Oral & Written Communications Content Discussion in class and problem solving on exams Attendance Mandatory. You are responsible for all the material covered in class as well as

all announcements, whether you are present or not. Evaluation Two in-class exams plus a mid-term exam and a final exam. Each exam

counts for 20% of the students' final grade. The last 20% are provided by the participation. Each in-class exam date will be announced in class two weeks prior to the exam. The mid-term and final exams will be given on the date announced on the web site.

STATISTICS Course Syllabus

Second Semester 2006-2007—Paris Course Title Statistics Instructors Dr. B. De Meyer E-mail [email protected] Course Objective Required Texts and References

J. Shao : Mathematical statistics, New York, Springer texts in statistics, 2003 A. Zaman : Statistical foundations for Econometric, London, Academic Press, 1996.


1) Reminder on orthogonal projections, 2) Reminder of Probability theory : Independence, Conditional expectation, Gaussian vectors, Limit theorems. 3) The general problem of statistics Estimation, Hypothesis testing, Parametric, Non-parametric 4) Sufficient statistics and the exponential model. 5) Moment estimators, Maximum likelihood estimators, asymptotic properties. 6) Estimators in the Linear Model 7) Fisher information, Rao Cramer Theorem, Lehman Sheffe theorem 8) Confidence interval, pivotal statistic, 9) Hypothesis testing : types of error, power function of a test. uniformly more powerful test, Maximum likelihood ratio, Asymptotic properties Neyman Person Test 10) Hypothesis testing in the linear model : variance analysis,




OPTIMIZATION AND DYNAMICS

Course Syllabus Second Semester 2006-2007—Paris

Course Title Optimization and Dynamics Instructors J. Blot and J.-B. Baillon E-mail [email protected], [email protected] Course Objective The main objective of this course is to master the use of optimization in dynamic

systems that are used in economics and other subjects. Required Texts and References

No required texts.

Description The course is divided into three main parts: Dynamic Systems with Continuous

Time, Dynamic Systems with Discrete Time, and Introduction to Dynamic Optimization.

Course Content

1) Dynamical Systems Section 1: Basic notions for discrete-time dynamical systems. Solutions, stationalry points, periodic points, various kinds ofstability Section 2: First-Order linear systems 2.1 Two-dimensional systems 2.2 Finite-dimensional systems 2.3 Asymptotic stability of the origin 2.4 Phase portraits 2.5 Scalar second-order linear systems 2.6 Samuelson oscillator Section 3: First-order nonlinear systems 3.1 Phase portraits 3.2 Local asymptotic stability of a stationary point 3.3 The second method of Liapunov 3.4 Linearization 3.5 A Hartman theorem 3.6 Chaotic behaviors Section 4: Basic notions for ordinary differential equations. Solutions, Cauchy problems Section 5: Flow associated to an ordinary differential equation 5.1 Global behavior of an nonextendable solution 5.2 Continuous dependence 5.3 Differential dependence Section 6: Linear ordinary differential equations 6.1 Resolvent 6.2 Exponential of matrices 6.3 Variation of constants

6.4 Scalar second-order linear ordinary differential equations Section 7: Stabilities 7.1 The various kinds of stability 7.2 Linear cases 7.3 Linearization 7.4 The second method of Liapunov 7.5 The Hartman-Grobman theorem

2) Discrete-time optimal control

Section 8: Controlled discrete-time dynamical systems 8.1 Basic notions 8.2 Controllability Section 9: Variational problems 9.1 Basic notions in finite horizon and infinite horizon 9.2 Necessary conditions 9.3 Sufficient Conditions Section 10: The problems of optimal control 10.1 Open-loop and non open-loop problems 10.2 The various kinds of optimality Section 11: The Pontryagin principles 11.1 Finite-horizon problems 11.2 Infinite-horizon problems 11.3 Sufficient conditions Section 12: The Bellman principles 12.1 The optimality principle 12.2 The Hamilton-Jacobi-Bellman equations 12.3 Relations between the principles of Pontryagin and Bellman




Optimization and DynamicsCourse Syllabus

Summer Term 2007 — Bielefeld

Course Title Optimization and Dynamics

Instructors Peter Zeiner

E–Mail [email protected]

Course Objective The course gives an introduction to dynamical systems (discreteand continuous). Students shall learn the basic quantitative andqualitative methods to solve dynamical sytems and shall becomeacqainted with the typical phenomena arising in linear and non–linear systems.

Prerequisits first courses in linear algebra and analysis

References R. L. Devaney, An Introduction to Chaotic Dynamical Systems,Addison–Wesley, 1989D. K. Arrowsmith, An introduction to dynamical systems, Cam-bridge Univ. Press , 1994additional ones may be given in the lecture

Description discrete and continuous dynamical systems, linear and non–linear,stability, bifurcations, chaos

Tentative content will be adapted according to the knowledge and needs of the stu-dents, some items may be added or skipped.dynamical systems with discrete time:one–dimensional systems and n–dimensional systemslinear and non–linear systemsstabilitybifurcationsperiod doublingchaosdynamical systems with continuous time:linear di!erential equationsnon–linear autonomous di!erential equationsexistence and uniqueness of solutionsstabilityflowPoincare mapsbifurcationhomoclinic pointschaos

Teaching Method Lecture, exercises (tutorial)

Attendance recommended, every week excercises have to be calculated, at leasttwo times during the semester an exercise has to be presented atthe blackboard.

Evaluation Final exam at the end of the semester; Students must solve exercisesevery week and must obtain at least 50% of the points in total.

MATHEMATICS FOR ECONOMISTS Course Syllabus

Second Semester 2006-2007—Paris Course Title Mathematics for Economists Instructors Dr. B. Cornet and Dr. L. Ménager E-mail [email protected], [email protected] Course Objective This course presents some complements of mathematics for economists, which

are not covered in the courses of Optimization, Dynamic Optimization, Probability and Statistics.


[1] Mathematics for Economists, C. Simon and L. Blume, Norton. Ch. 10, 16, 23. [2] De La Fuente, A., Mathematical Methods and Models for Economists, 2nd Ed. (2005) Cambridge University Press.

Description This course contains four main sections: Normed and Metric Space R^n, Euclidian

Space R^n, Dual Space, and Compact Metric Spaces. Course Content

1. The normed and metric space R^n. The space R^n as a metric space, axioms of the distance, converging sequences, closed and open balls, closed and open sets, closure, interior and boundary of a set. (Semi-)continuous functions, homeomorphisms. Cauchy sequences, complete spaces, completeness of R^n, Fixed-point of contractions. The space R^n as a normed space, axioms on the norm, distance associated with a norm, examples of distances which are not associated with any norm. Equivalent norms, equivalent distances and consequences for Cauchy and convergent sequences. The normed space of linear mappings, every linear mapping between R^n and R^m is continuous. 2. The Euclidean space R^n. Scalar product of a pre-Hilbert space, Euclidean spaces, matrix representation, Examples. Cauchy-Schwarz inequality, Norm associated to a scalar product and its characterization. Orthogonality and polarity, Orthogonal basis, Gram-Schmidt orthogonalization process, orthogonal projection and projection on a convex, geometric interpretation. Adjoint of a linear mapping and the relationship with the transpose mapping. Bilinear forms, matrix representation, symmetric and alternating bilinear forms, quadratic forms. (Semi-) definite quadratic forms, the 2x2 case, linear constraints and bordered matrices. Diagonalizing real symmetric matrices. 3. Dual Space Linear functionals and the dual space, dual basis, second dual space, orthogonal subspace, transpose of a linear mapping, link with the adjoint mapping. Isomorphism of vector space with its dual space in finite dimension. 4. Compact Metric Spaces Subsequences and properties. Borel-Lebesgue defintion of compactness, properties of compact spaces. Bolzano-Weierstrass characterization, finite interesction property, and characterization in R^n. Compactness and the extreme value theorem (Wierstrass). Continuous functions on compact spaces. Equivalent norms. The Riesz’ theorem. Locally compact spaces.

Teaching Method Lecture, discussion and problem solving

Oral & Written Communications Content Discussion in class and problem solving on exams Attendance Mandatory. You are responsible for all the material covered in class as well as all



MATHEMATICS FOR ECONOMISTS Course Syllabus

Second Semester 2007—Bielefeld Course Title Mathematics for Economists Instructors Prof. Walter Trockel and Ph.D Students E-mail [email protected] Course Objective The course offers a summery of mathematical basics necessary to understand the

quantitive methods of economic theory. The course is designed to provide students with a good mathematical background and participation is voluntary.

Required Texts and References Novshek, William – Mathematics for Economists Description Basic Course Content - Calculus of one Variable (Differentiation, Integration)

- Linear Algebra (Scalar Product, Eigenvalues, Quadratic Forms, Semidefinite Matrices)

- Correspondeces (Maximum Theorem, Continuity) - Calculus of several Variables (Gradients, Taylor’s Theorem, Optimization with

and without constraints, Duality) - Nonlinear Programming - Comparative Statics (Envelope Theorem, General Procedure, Interpretation of Lagrange multipliers, Application to Consumer Theory) - Line Integrals -Stability -Dynamic Programming

Teaching Method Reading Course Oral & Written Communications Content Discussion in class Attendance Not mandatory. The course is an offer to provide all students with a strong

mathematical background. Evaluation no evaluation

APPLIED ECONOMETRICS Course Syllabus

Second Semester 2006-2007—Paris Course Applied Econometrics Instructor Faye Steiner E-mail [email protected] Course Objective Students should be able to use data and build statistical models to approach

economic questions. Texts and References

No required text. All of the econometric concepts treated in the course can be found in Basic Econometrics, Damodar N. Gujarati, McGrawHill. A more mathematical treatment may be found in Econometric Analysis, Williame Greene, Pearson Education.

Description The purpose of this course is to engage students in direct, "hands-on" empirical

applications of econometric tools using actual contemporary datasets and software. Students will use data on asset prices and the statistical package Stata to test the Capital Asset Pricing Model (CAPM) theory. Econometric concepts treated in the course include descriptive analysis, bivariate regressions, hypothesis testing and goodness of fit, event studies, structural change and specification tests, heteroskedasticity, and autocorrelation.

Teaching Method Students will work in a computer lab under the guidance of the instructor. Attendance Required. More than two absences will result in a zero participation grade and a

high risk of failing the class. Evaluation Participation 20% Problem Sets 30% Final Exam 50% Exam Date The final exam will be given in class on the last day of class, March 29, 2007 8h -

12h.

microeconomics 1 course syllabus first … › img › pdf › syllabi_all_2006_2007.pdfdavid romer,...

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