Economics, Management and Data Science

The course deals with some fundamental topics in Microeconomics. It aims at bringing the students from an intermediate to an advanced level of exposure and understanding of the material. The course will give emphasis to problem solving. For this reason problem sets will be assigned during the course at dates to be communicated in class. Students will then rotate on the board in a following lecture to discuss the problems. Problem sets will not be marked but discussion will be taken into consideration in the final evaluation (30%).

The sequence in macroeconomics will introduce students to the literature that studies the aggregate evolution of the economy both in the short and long run. A particular emphasis will be given to the role of institutions in explaining economic performance in the long run. The role of monetary policies for the short-run evolution of the economic cycle will be addressed in the last module of the sequence.

Part 1 (D. Ticchi)
-Traditional Keynesian Theories of Fluctuations
-The Lucas Imperfect-Information Model and The Lucas Critique
-Consumption

This course deals with the following topics:

1) Regression and Causality: a) Properties of the Conditional Expectation Function; b) Bad controls; c) Omitted variable bias; d) Measurement errors; e) Simultaneous equations; f) How to write an empirical project.

Empirical studies on heterogeneous firms (F. Pammolli, A. Rungi):

Discrete-time optimal control: dynamic programming for finite/infinite horizon and deterministic/stochastic optimization problems. LQ and LQG problems, Riccati equations, Kalman filter. Deterministic continuous-time optimal control: the Hamilton-Jacobi-Bellman equation and the Pontryagin?s principle. Examples of optimal control problems in economics.

The course introduces numerical methods for the approximate solution of initial and boundary value problems governed by linear partial differential equations (PDEs) ubiquitous in physics, engineering, and quantitative finance. The fundamentals of the finite difference method and of the finite element method are introduced step-by-step in reference to exemplary model problems related to heat conduction, linear elasticity, and pricing of stock options in finance. Notions on numerical differentiation, numerical integration, interpolation, and time integration schemes are provided.

The course is structured into three modules: the first one will cover advanced topics in complex network theory, whereas, the second one will focus on economic and financial networks, dealing with both theory and applications.

Module 1: Advanced Theory of Complex Networks
Lecture 1 Models of Evolving Networks
Lecture 2 Fitness & Relevance models
Lecture 3 The Master Equations approach
Lecture 4 Percolation
Lecture 5 Epidemic Models on Networks
Lecture 6 Advanced Topological Properties
Lecture 7 Complex Networks Randomization

Basics of pattern recognition and machine learning and real world applications in imaging, internet, finance. Similarities and differences. Supervised vs unsupervised learning. Linear regression in many ways. The logistic regression. Support vector machines for classification and regression. Random Forests for classification. Linear and quadratic discriminant analysis. Unsupervised learning (k-means, c-means, kernel k-means, spectral clustering, EM). Feature extraction and selection (PCA, ICA, kernel PCA, and manifold learning). Current trends in Machine Learning.

The course provides an introduction to dynamical systems, with emphasis on linear systems. After introducing the basic concepts of stability, controllability and observability, the course covers the main techniques for the synthesis of stabilizing controllers (state-feedback controllers and linear quadratic regulators) and of state estimators (Luenberger observer and Kalman filter). The course also covers data-driven approaches of parametric identification to obtain models of dynamical systems from a set of data, with emphasis on the analysis of the robustness of the estimated models w.r.t.

This course aims at introducing, from an advanced point of view, the fundamental concepts of probability and statistical inference.
Some proofs are sketched or omitted in order to have more time for examples, applications and exercises. In particular, the course deals with the following topics:

? probability space, random variable, expectation, variance, cumulative distribution function, discrete and absolutely continuous distributions, random vector, joint and marginal distributions, joint cumulative distribution function, covariance,