PhD in Economics and Management

Availability

The course is intended for 1st year students on PhD in Economics and Management.

Pre-requisites

Introduction to mathematics, elementary statistical theory and elementary set theory. Basic knowledge of probability theory, as in: P. Newbold, W. Carlson, B. Thorne (2012), Statistics for Business and Economics, Pearson Higher Education, Chapters 3-5 (previous editions would be fine as well). Attendance at more advanced courses such as real analysis, probability, distribution theory and statistical inference would be desirable.

Objectives of the course

The purposes of this course are: (i) to explain, at an intermediate level, the basis of probability theory and some of its more relevant theoretical features; (ii) to explore those aspects of the theory most used in advanced analytical models in economics and finance. The topics will be illustrated and explained through many examples.

Program

Course content

1. Algebras and sigma-algebras, axiomatic definition of probability, probability spaces, properties of probability, conditional probability, Bayes theorem, stochastic independence for events.
2. Random variables, measurability, cumulative distribution functions and density functions.
3. Transformations of random variables, probability integral transform.
4. Lebesgue integral, expectation and variance of random variables, Markov inequality, Tchebycheff inequality, Jensen inequality, moments and moment generating function.
5. Multidimensional random variables, joint distributions, marginal and conditional distributions, stochastic independence for random variables, covariance and correlation, Cauchy-Schwartz inequality.
6. Bivariate normal distribution, moments, marginal and conditional densities.
7. Transformations of multidimensional random variables.
8. Convergence of sequences of random variables, weak law of large numbers and central limit theorem.

Textbook

S. Ross (2010). A First Course in Probability, 8th Edition. Pearson Prentice Hall.

Further readings

G. Casella, R. L. Berger (2002). Statistical Inference, Second edition. Duxbury Thompson Learning.
R. Durrett (2009). Elementary Probability for Applications. Cambridge University Press.
M. J. Evans, J. S. Rosenthal (2003). Probability and Statistics - The Science of Uncertainty. W. H. Freeman and Co.
G. Grimmett, D. Stirzaker (2001). Probability and Random Processes. Oxford University Press.
A. M. Mood, F. A. Graybill, D. C. Boes (1974). Introduction to the Theory of Statistics. McGraw-Hill.
P. Newbold, W. Carlson, B. Thorne (2012). Statistics for Business and Economics. Pearson Higher Education.
D. Stirzaker (2003). Elementary Probability. Cambridge University Press.
L. Wasserman (2004). All of Statistics. Springer.

Advanced readings

R. B. Ash, C. A. Doléans-Dade (2000). Probability and Measure Theory. Harcourt/Academic Press.
M. J. Schervish (1995). Theory of Statistics. Springer.

Reference texts
Author	Title	Publishing house	Year	ISBN
S. Ross	A First Course in Probability (Edizione 8)	Pearson Prentice Hall	2010
L. Wasserman	All of Statistics	Springer	2004
D. Stirzaker	Elementary Probability	Cambridge University Press	2003
R. Durrett	Elementary Probability for Applications	Cambridge University Press	2009
A. M. Mood, F. A. Graybill, D. C. Boes	Introduction to the Theory of Statistics	McGraw-Hill	1974
R. B. Ash, C. A. Doléans-Dade	Probability and Measure Theory	Harcourt/Academic Press	2000
G. R. Grimmett, D. R. Stirzaker	Probability and Random Processes (Edizione 3)	Oxford University Press	2001	0198572220
M. J. Evans, J. S. Rosenthal	Probability and Statistics - The Science of Uncertainty	W. H. Freeman and Co.	2003
G. Casella, R. L. Berger	Statistical Inference (Edizione 2)	Duxbury Thompson Learning	2002
P. Newbold, W. Carlson, B. Thorne	Statistics for Business and Economics	Pearson Higher Education	2012
M. J. Schervish	Theory of Statistics	Springer	1995

Examination Methods

A two-hour written paper at the end of the course.

Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE

PhDs

Training and Research

PhD Programme Courses/classes

Academic writing in latex and academic presentation

Advanced English for Academic Skills

Agenda dell’organizzazione delle nazioni unite 2030 sullo sviluppo sostenibile, ricerca e diritto antidiscriminatorio: strumenti ed esperienze nelle università

Artificial intelligence, cybersecurity e diritto

Behavioral and Experimental Economics

Comunicare la scienza: il ruolo dei ricercatori e il rapporto tra esperti, cittadini e istituzioni

Corporate Governance

Corso di inglese B1/certificazione B1

Corso di inglese B2/certificazione B2

Corso di inglese C1/certificazione C1

CORSO DI LINGUA ITALIANA PER STRANIERI

Corso di programmazione con matlab

Medical statistics with R

Basic statistics course

Intermediate statistics course

(Meta-analysis using the statistical software Stata and R

Corso teorico-pratico di microscopia di base

Development economics

Diritto d'autore e brevetti

Dissemination dei risultati della ricerca

Econometrics for management

Economia dei Mercati Energetici

English for academic presentations

English for academic writing

Finanza

Game Theory

Inequality

Introduzione al “public speaking”

La mia archeologia e la mia politica culturale

Python programming language

Macro economics

Mathematics

Microeconomics 1

Organization Theory

Political economy

Presentation of Horizon Europe framework programme

Probability

Project writing for beginners

Qualitative methodologies in management studies

Quantitative methodologies in management studies

Seminario Consigliera di fiducia

Software R

Spin off e start-up innovative

Statistica

Supply Chain Management

Protecting psychological well-being in the PhD program: development and enhancement of personal strategies and attitudes that predispose to professional satisfaction and ethical collaboration.

Probability (2020/2021)

Learning outcomes

Program

Examination Methods

Univr risponde - Assistente Virtuale

Univr risponde