I TERM September-December


Homogeneous functions and Euler’s formula. Continuous functions and compact sets. Concave and quasi concave functions. The implicit function theorem. Convex sets and separating hyperplanes: separating hyperplanes theorem, supporting hyperplanes theorem. Difference equations. Unconstrained maximization: local and global maximizer (minimizer), maximization theorems. Constrained maximization: the Lagrangian function and constraints qualification, Lagrange multipliers. Inequality constraints: Kuhn Tucker conditions. Comparative statics. Differential equations and systems of differential equations. Dynamic maximization: the calculus of variations and its applications to economic models, Euler equation of maximization problems . Control theory and applications to economic models.  


  • Alpha C. Chiang and Kevin Wainwright, "Fundamental Methods of Mathematical Economics", New York, Mc-Graw Hill - Irwin.
  • Peter Hammond, Knut Sydsaeter, Atle Seierstad and Arne Strom, "Further Mathematics For Economic Analysis", 2nd Edition, Pearson Education 2008

  • GAME THEORY (Prof. Marco Pagnozzi)
Static games with complete information. Simultaneous moves games. Games in strategic form, dominant strategy equilibrium, iterated deletion of strictly dominated strategies. Reaction functions and Nash equilibrium. Finding Nash equilibria with both discrete and continuous action spaces. Supermodular and submodular games. Mixed strategies, domination by a mixed strategy and never-best-response. Rationalibility. Imperfect Information and incomplete information. Risk dominance. Dynamic games with complete information. Games in extensive forms. Backward induction and information sets, Subgame perfect Nash equilibrium. Repeated games. Folk theorems. Collusion. Games with incomplete information. Bayesian Nash Equilibrium. Purification. Forward induction. Sequential rationality, consistency of beliefs and perfect Bayesian Nash Equilibrium. Signalling: separating equilibria and pooling equilibria. Spence Signalling Model. Cho and Kreps criterion.

  • Robert Gibbons, "A Primer in Game Theory", Harvester-Wheatsheaf, 1992
  • Martin Osborne, "An introduction to Game Theory", Oxford University Press, 2003
  • Andreu Mas-Colell, Michael Whinston e Jerry R. Green, "Microeconomic Theory", Oxford University Press, 1995. 

  • MICROECONOMICS I (Prof. Giovanni Andreottola)
Reference and choice: preference relations, choices rules, the consumption set, competitive budgets, demand functions and comparative static. Preference and utility. The utility maximization problem. The expenditure minimization problem. Duality. Indirect utility and expenditure function. Integrability. The weak axiom of revealed preferences. The strong axiom of revealed preference. Welfare evaluation and economic changes. Aggregate demand and wealth. Production: production set, profit maximization and cost minimization, efficient production. Choice under uncertainty: expected utility theory, money lottery and risk aversion, state dependent utility. Monopoly. Oligopoly. General equilibrium theory: pure exchange, Edgeworth box, consumer-producer economy. 
  • Hal R. Varian, "Microeconomic Analysis", W. W. Norton & Company, 3rd edition, 1993.
  • Andrew Mas-Colell, Michael D. Whinston and Jerry R. Green, "Microeconomic Theory", Oxford University Press, 1995.


The course is an introduction to the classical statistical inference theory. The first half of the course is devoted to Probability theory. Topics include: Elements of set theory. Axiomatic definition of probability. Calculus of probability. Conditional probabaility and Bayes Theorem. Discrete and continuous random variables. Common Family of distributions, Hierarchies and Mixtures. Bivariate Random variables. Transformations and Convolution Integral. The second part of the course is devoted to Inference. Topics include: Sampling and sampling distribution. Principles of data reduction (sufficiency, Likelihood). Point and interval estimation (methods to find estimators and properties of the estimators). Hypothesis testing. Asymptotic Theory. Linear regression models. The very last lectures are devoted to an introduction to the use of Stata for applied economic research. 


  • Casella, G. and Berger, R: "Statistical Inference", Duxbury press.
  • Stock, J and Watson, M: "Introduction to Econometrics", Addison-Wesley.

II TERM January-March

  • ASSET PRICING (Prof. Lorenzo Pandolfi – Prof. Giovanni W. Puopolo)

Functions of financial markets. Model of consumption and investment choice in autarchy and with perfect financial markets: Fisher’s separation theorem. Consumption and investment with imperfect financial markets. Choices under risk: expected utility, attitudes to risk, risk premium, HARA utility, comparing risk (first order stochastic dominance, second order stochastic dominance). Intertemporal choice under uncertainty and asset pricing: introduction. Contingent claims markets: law of one price, arbitrage, complete markets and state prices, relation between state prices and asset prices, equilibrium state prices, risk neutral probabilities. Mean-variance analysis: efficient frontier with N risky assets, two-fund separation theorem, tangency portfolio, market equilibrium (CAPM) without and with a riskless asset, extensions of the static CAPM. Consumption-based asset pricing: Merton’s intertemporal CAPM, Lucas model, equity premium puzzle. Empirical evidence: testing the CAPM and the CCAPM. Bond pricing and term structure of interest rates. Market efficiency and investor rationality.


  • John H. Cochrane, "Asset Pricing", Princeton University Press;
  • Jean-Pierre Danthine and John B. Donaldson, "Intermediate Financial Theory", Prentice Hall 2002.

  • MICROECONOMICS II (Prof. Riccardo Martina – Prof. Giovanni Immordino)
The course will focus on Economics of information. One economic agent has often more information about a characteristic that is relevant to an agreement, than the other. In this module, we will study how agents deal with this information asymmetry by designing incentives and embedding them in contracts. We will also study the effects of information asymmetry on the prevailing market equilibrium. Applications of the theory include insurance, labour economics, industrial economics. By the end of the module, students should be familiar with the different types of information asymmetries and their consequences in contract design and market equilibrium and should be able to solve principal-agent models using appropriate mathematical techniques.
  1. Introduction
  2. The types of asymmetric information
  3. The basic principal agent model; Description of the model; Symmetric information contracts
  4. The moral hazard problem; The case when the agent chooses between two effort levels; Continuous effort; Applications
  5. The adverse selection problem; A model for one principal and one agent; When principals compete for agents; Applications 


  • Bolton, P and Dewatripont, M "Contract Theory", The MIT Press, 2005
  • Macho-Stadler, I and Perez-Castrillo, J.D "An introduction to the Economics of Information Incentives and Contracts", Oxford University Press, 2001
  • Salanie, B. "The Economics of Contracts" MIT Press, 2005.

  • MACROEONOMICS I (Prof. Tullio Jappelli - Prof. Salvatore Capasso)

The Solow growth model. The Ramsey-Cass-Koopmans model. The Diamond model. Cross country income differences. Consumption under uncertainty: permanent income/random walk hypothesis. Investments: a model of investment with adjustment costs, Tobin’s Q. Real business cycle theory: a baseline Real-business Cycle model. Inflation and monetary policy: inflation money growth and interest rates, the dynamic inconsistency of low-inflation monetary policy, addressing the dynamic inconsistency problem.


  • David Romer, "Advanced Macroeconomics", fourth edition, Irwin/McGraw-Hill, 2001;
  • Oliver Blanchard and Stanley Fisher, "Lectures on Macroeconomics", MIT Press, 1990;
  • Robert Barro and Xavier Sala-i-Martin, "Economic Growth", McGraw-Hill, 1995;
  • Philippe Aghion and Howard Howitt, "The Economics of Growth" MIT Press, 2009

  • ECONOMETRICS (Prof. Pietro Coretto)

Classical multiple linear regression model: ordinary least squares (OLS), goodness of fit and analysis of variance. Finite sample properties of the OLS estimator: unbiased estimation, variance of the OLS estimator and the Gauss Markov theorem. Estimation of the variance of the least square estimator. Normality assumptions and basic statistical inference. Data problems: multicollinearity and missing observations. Large sample properties of the OLS estimator: consistency, asymptotic normality, asymptotic efficiency. Instrumental Variables and Hausman’s specification test. Inference and Prediction. Tests for structural change: dummy variables, partitioned regression. Specification analysis and model selection: irrelevant variables and omission of relevant variables. Nonspherical disturbances and generalized regression model: GLS and FGLS. Heteroskedasticity: inefficiency of OLS, estimated covariance matrix of the parameters, Generalized Method of Moments (GMM), estimation of the heteroskedastic regression model, testing for heteroskedasticity. Serial Correlation: disturbance processes, testing for autocorrelation; models with lagged variables.


  • William H. Greene, "Econometric Analysis", Pearson Education,2003

III TERM April-June

  • DERIVATIVES (Prof. Giuliano Curatola)
Forward contracts. Futures contracts. Options. Other derivatives. Hedging strategies using futures: minimum variance hedge ratio. Stock index futures. Interest rate markets: zero rates, bond pricing, forward rates, forwards rates agreements. Theories of term structure. Treasury bond futures. The LIBOR zero cure. Duration, duration based hedging strategies. Swaps: swap quotes and LIBOR zero rates, valuation of interest rate swaps, valuation of currency swaps. Mechanics of option markets: specification of stock options, trading commissions and margins, taxation. Warrants, executive stock options and convertibles bonds. Properties of stocks options: factors affecting options prices, put-call parity, effect of dividends. Trading strategies involving options: strategies involving a single option and a stock, spreads, combinations. Binomial trees: risk neutral valuation. Models of behaviour of stock prices: Markov property, continuous time stochastic process, process for stock prices, Itô’s Lemma. Lognormal property of stock prices. Distribution of the rate of return. Derivation of the Black-Scholes-Merton differential equation, Black-Scholes pricing formula, cumulative normal distribution functions, options pricing formulas. Currency options. “The Greeks”: Delta, Theta, Gamma, Rho, Vega. 


  • John C. Hull, "Options futures and other derivatives", Prentice Hall, 2005.

  •  TIME SERIES ECONOMETRICS (Prof. Antonio Acconcia)
The main purpose of the course is to provide an introduction to estimation ant testing of dynamic causal effect. The pre-requisites include a good knowledge of the OLS estimator under classical assumption and a basic knowledge of the IV estimator.

Intoduction: review of OLS and finite sample results. Conditional density function, Strict Exogeneity, Conditional homoschedasticity, Absence of conditional serial correlation, Gauss-Markov theorem, Frisch-Waugh theorem, Testing hypothesis about population parameters.

Basic concepts for time series econometrics: DGP, Sequential factorization, Serial correlation, Distributed lag model, Dynamic causal effect, Method of Moments estimator and GMM, Deterministic trend, Filter, Structural change an Chow rtest.

Single equation models: OLS and large sample results: Stationarity, Ergodicity, Martingale Sequence, Limit theorems, Limit distribution of OLS for stationary stochastic process, Complete dynamic specification, Mean trend process, Econometric models with serially correlated errors. A loook at instumental variable regression: OLS versus IV for large sample, The 2SLS estimator, Hausman test, Sargan-Hansen test. Covariance-stationary process: Impulse response function, Wold decomposition theorem, VAR - Dynamic causal effect for equation system, Structural interpretation of VAR. Introduction to non-stationary process: Unit root process, Dickey-Fuller test, Cointegration. 


  • Hayashi Fumio, "Econometrics" (2000), Princeton University Press


This course introduces and develops an economic framework for business analysis and valuation. This framework covers key valuation components such as financial accounting data, business strategy and cash flows. The framework is then applied to a variety of decision contexts including valuation, mergers and acquisitions, and private equity deals. Each of the topics introduced in this course covers both institutional details and results of relevant academic research. It is furthermore supported by case studies. The course should thus appeal to students intereseted in equity research, corporate finance, business strategy and private equity.The course is primarily based on lecture notes, articles and readings.

  • CORPORATE FINANCE (Prof. Annamaria Menichini)

Capital structure theory with symmetric information: valuation of the firm, M&M propositions, M&M with taxes, M&M with taxes and bankruptcy, Miller equilibrium, DeAngelo and Masulis model. Capital structure with asymmetric information: credit and equity rationing, role of collateral, optimal capital structure with agency costs. Corporate governance. Dividend policy theory: dividend indifference, types of dividend policy, tax effects, signalling theories of dividend policy. Initial Public Offerings: IPO underpricing.


  • Richard A. Brealey and Stewart C. Myers, "Principles of Corporate Finance", McGraw-Hill, 7th edition, 2003;
  • Jean Tirole, "The Theory of Corporate Finance", 2005, Princeton University Press.

  • MACROECONOMICS II (Prof. Saverio Simonelli)

The course covers the basic real business cycle model and then moves to New-Keynesian models. It discusses the microeconomic foundations of nominal rigidities, analysing models of imperfect information and models of imperfect competition with menu costs and real rigidities. Finally, we discuss unemployment fluctuations and cycles driven by self-fulfilling expectations in non-walrasian models with coordiantion failures and multiple equilibria. The course is composed of four parts: 

- Part 1 covers the stylized of the business cycle; 

- Part 2 is devoted to real business cycle models;

- Part 3 covers the microfoundations of nominal rigidities, namely (i) imperfect information, (ii) imperfct competition and flexible prices, including the role of menu costs, (iii) imperfect competition and predetermined prices, (iv) imperfect competition and state-dependant pricing;

- Part 4 of the course analyses non Walrasian models that generate (i) strategic complementarities and multiple equilibria; (ii) unemployment fluctuations and labour market dynamics. 


  • David Romer, "Advanced Macroeconomics", McGraw Hill 2006
  • Fabio-Cesare Bagliano and Giuseppe Bertola, "Models for Dynamic Macroeconomics", Oxford University Press, 2004


This course provides a rigorous treatment of advanced concepts of equity and fixed income investments. These are some (not all) of the major areas we will be looking at: Arbitrage and limits to arbitrage, hedge funds and their performance, equity premium and its evolution through time, asset pricing models (especially multi-factor models), methods to generate the yield curve and term structure of interest rates from real-life bonds, convexity and duration of bonds, bond investment strategies, bonds with embedded options, securitization and mortgage backed securities.


  • "Investments" by Bodie, Kane and Marcus
  • "Bond Evaluation, Selection and Management" by Johnson

  •  BANKING (Prof. Alberto Zazzaro)
Banking is an ever expanding field of theoretical and empirical research in economics. The purpose of the course is to provide an introduction to the economics theory of banking and to discuss some empirical issues. Pre-requisites are a basic knowledge of game theory, contract theory, industrial organization and econometrics. The course covers four main topics: the role and function of financial intermediaries; Bank-firm relationships; Credit market competition and bank stability; Bank regulation.


  • X. Freixas and J.J Rochet, Micoreconomics of Banking, the MIt press, second edition, 2008. Journal articles will be indicated during the course.  

  • MARKET MICROSTRUCTURE (Prof. Marco Pagano)
The topic of the course is liquidity and price formation on securities markets. The structure and performance of prominent real-world securities markets is described and examined using relevant theory and evidence from the financial economics literature. The course focuses on stock market microstructure, that is, secondary market trading strategies and trading costs; how trading on stock exchanges is organized and regulated, and how this affects their functioning in terms of trading costs, international efficency, volatility and other measures of performance. The impact of differences in trading system architecture and regulatory policies is considered. Explicit attention is also given to the relationship between market liquidity and asset prices, highlighting the role of the liquidity of the secondary market in determining the cost of new capital.

The course is primarly based on lecture notes, articles and readings. 

  • DEVELOPMENT ECONONIMCS I (Prof. Shanker Satyanath)

The question of why some countries stagnate economically while others grow rapidly has long been one of most important questions in the field of Economics. It is now widely acknowledged that politics plays a central role in influencing growth. This has made the political economy of economic development one of the cutting edge areas of research in Political Science as well. The goal of this course is to familiarize students with the current frontiers of research in the political economy of development, taking full account of the multi-disciplinary nature of the field. Accordingly, the reading list primarily focuses on recent publications and working papers, which span the fields of Political Science as well as Economics.

The professor will provide the necessary historical context when required.

  • LAW AND ECONOMICS (Prof. Marcello Puca )

The course examines both traditional and current topics in the field of law and economics. Classes focus on existing legal theories and on their applications in economics, covering the economic analysis of legal institutions, property law, tort law and contract law. The purpose of the course is to provide students with basic concepts in the economic analysis of law, with specific focus on empirical legal studies and behavioral law and economics. The course is aimed both at students willing to pursue an academic career or to those interested in working in the consultancy industry or in regulatory authorities.

  • ECONOMIC THEORY (Prof. Vincenzo Platino)
The first part of the course focuses on Consumption theory, testable restrictions (Slutsky matrix, Afriat's Theorem and GARP) and Collective Consumption Models. Furthermore, the course will also provide a brief overview of the Theory of General Economic Equilibrium from a differentiable approach and the Theory of Regular Economics. The second part of the course will introduce the Theory of Two-Sided Matching. It will analyze matching mechanisms for two sided market structures and study their main properties (e.g., stability, efficiency and strategy-proof).


  • Revealed Preference Theory, Christopher P. Chambers and Federico Echenique.
  • Economics of the Family, Martin Browning, Pierre-André Chiappori, Yoram Weiss.
  • Differential Topology and General Equilibrium with Complete and Incomplete Markets, Antonio Villanacci, Laura Carosi, Pierluigi Benevieri, Andrea Battinelli.
  • Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysi, Alvin E. Roth, Marilda A. Oliveira Sotomayor.
  • Matching, Allocation, and Exchange of Discrete Resources, Tayfun Sönmez and M. Utku Ünver. HANDBOOK OF SOCIAL ECONOMICS

  • BANKING REGULATION (Dott. Roberto Mosca)

Understanding the basics principles of banking regulation and supervision is central for everyone either targeting a career in a central bank or seeking a job in any credit institution. At the same time it could be relevant for students interested in banking and finance for research purposes. Purpose of the course is to give an overview of the current framework of the banking micro-supervision exploring its economic rationale, highlighting the pillars of the current framework and possibly its future evolution. Provided that risk management systems within credit institutions endogenously result from the interaction of banking regulations, active supervisions and business needs, an overview of the best practices expected and required to large and complex banks will be provided too. Course will be held by practitioners as most of the speakers have a background in banking supervision. Focus will be mostly on common practices rather than on theory. At the end of the course each student will have improved its understanding of the current framework for prudential regulation centered around capital requirements. At the same time they will have gained better comprehension of risk management practices within banks.

  • MICROECONOMETRICS AND PANEL DATA (Prof. Annalisa Scognamiglio)
We will study how microeconomic data on individual economic agents can be used to draw inferences on their behaviour. The course will focus on the econometric methods that economists use for empirical microeconomic research. This will include the study of econometric models with limited dependent variables, models of selection and censoring. Particular emphasis will be given to the policy evaluation methods. The focus will primarily be on parametric models, but there will be some discussion of semi-parametric models. Along the way, we will discuss application of these models to economic data in contemporary empirical research. This will illustrate how microeconometric methods can be employed to answer real-world questions of economic interest.

Practical tutorials will be an essential part of this course. STATA will be the standard software both for practical tutorials and problem sets.


  • Jeffrey M. Wooldridge, Econometric Analysis of Cross Section and Panel Data, MIT Press, 2002.
  • Richard Blundell and Monica Costa-Dias, “Alternative Approaches to Evaluation”, CEF.UP Working Paper No. 0805, 2008.
  • Joshua Angrist and Joerg-Stephen Pischke, Mostly Harmless Econometrics, An Empiricist’s Companion, Princeton University Press, 2009.

  • AUCTION THEORY (Prof. Marco Pagnozzi)
The course introduces the main results of the economic literature on auctions, in order to provide an analytical framework for analyzing real-world auction markets. It discusses a number of practical applications that highlight the crucial elements of successful auction designs and bidding strategies. The course is designed for graduate students in economics and practitioners (economic consultants, regulators, central bankers, etc.) interested in understanding the design and functioning of auction markets.


  • Klemperer, P. (2004), “Auctions: Theory and Practice.” Princeton University Press.
  • Krishna, V. (2002), “Auction Theory.” Academic Press.


The aim of the course is to provide a foundation in development micro-economics and an introduction to current research in the field. Students will get acquainted with the theoretical and empirical tools used in the economic analysis of central issues in the developing country context (such as: fertility choices and demographic transition, demand- and supply-side factors in low educational attainment, innovations to overcome credit market failures for the poor, adoption and diffusion of technological change in agriculture). We will discuss policy options to address these issues, and empirical challenges in evaluating the effectiveness of such policy interventions; we will also examine recent developments, including effects of the ongoing Covid-19 pandemic (and its economic repercussions) in the course topic areas.

  • PSYCHOLOGY AND ECONOMICS (Prof. Antonio Rosato)

This subject explores ways that psychological research indicating systematic departures from classical economic assumptions can be translated into formal models that can be incorporated into economics. Topics include ways utility theory can be improved such as incorporating reference dependence, news utility, social preferences, self-image, and other belief-based tastes and ways we can relax assumptions of perfect rationality such as incorporating limited attention, biased prediction of future tastes, present-biased preferences, biases in probabilistic judgment, and errors in social inference. The course will emphasize (a) careful interpretation and production of new evidence on relevant departures, (b) formalizing this evidence into models that can, with discipline and rigor, generate sharp predictions using traditional economic approaches, and (c) exploring economic implications of those models presented. And while the course centres on theoretical models (learning and evaluation will centre around solving formal problem sets), the theory is focused on empirical implementability and economic relevance, so that the course is also designed for those interested in theory-influenced empirical research. The course focuses on formal modeling. The course will involve more words and more intuition and more classical middlebrow economic theory than the typical advanced-theory held course. It will, of course, involve more reading and discussion of the behavioural evidence and psychological foundations of our assumptions than do other theory (or non-theory) economics courses. But, in the end, its emphasis is on formal modeling.