Training and Research

PhD Programme Courses/classes - 2019/2020

Lezioni Dottorandi

Credits: 50

Language: Italian

Teacher:  Valeria Franceschi, Catia Scricciolo

Behavioral and Experimental Economics

Credits: 5

Language: Italian

Teacher:  Maria Vittoria Levati, Chiara Nardi, Luca Zarri

Corporate governance

Credits: 4

Language: Italian

Teacher:  Alessandro Lai

Development Economics

Credits: 4

Language: Italian

Teacher:  Federico Perali

Econometrics for management

Credits: 4

Language: Italian

Teacher:  Francesca Rossi, Laura Magazzini

Energy Economics

Credits: 2,5

Language: Italian

Teacher:  Luigi Grossi

Game Theory

Credits: 4

Language: Italian

Teacher:  Francesco De Sinopoli

Inequality

Credits: 5

Language: Italian

Teacher:  Francesco Andreoli, Claudio Zoli

Macro economics

Credits: 2,5

Language: Italian

Teacher:  Alessia Campolmi

Macroeconomics I

Credits: 10

Language: Italian

Teacher:  Claudio Zoli, Angelo Zago, Martina Menon

Mathematics

Credits: 7,5

Language: Italian

Teacher:  Alberto Peretti, Athena Picarelli, Letizia Pellegrini

Organization Theory

Credits: 4

Language: Italian

Teacher:  Cecilia Rossignoli, Alessandro Zardini, Lapo Mola

Political economy

Credits: 5

Language: Italian

Teacher:  Emanuele Bracco, Roberto Ricciuti, Marcella Veronesi

Probability

Credits: 7,5

Language: Italian

Teacher:  Marco Minozzo

Metodi quantitativi per la gestione aziendale

Credits: 5

Language: Italian

Teacher:  Riccardo Scarpa

Statistica

Credits: 7,5

Language: Italian

Supply Chain Management

Credits: 4

Language: Italian

Teacher:  Barbara Gaudenzi

Credits

7.5

Language

Italian

Class attendance

Free Choice

Location

VERONA

Learning outcomes

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 Notes
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

PhD school courses/classes - 2019/2020

PhD School training offer to be defined

Faculty

A B C D F G L M N P Q R S T V Z

Andreoli Francesco

symbol email francesco.andreoli@univr.it symbol phone-number 045 802 8102

Bracco Emanuele

symbol email emanuele.bracco@univr.it symbol phone-number 045 802 8293

Bucciol Alessandro

symbol email alessandro.bucciol@univr.it symbol phone-number 045 802 8278

Campolmi Alessia

symbol email alessia.campolmi@univr.it symbol phone-number 045 802 8071

Cipriani Giam Pietro

symbol email giampietro.cipriani@univr.it symbol phone-number 045 802 8271

Demo Edoardo

symbol email edoardo.demo@univr.it symbol phone-number 045 802 8782 (VR) 0444.393930 (VI)

De Sinopoli Francesco

symbol email francesco.desinopoli@univr.it symbol phone-number 045 842 5450

Fioroni Tamara

symbol email tamara.fioroni@univr.it

Franceschi Valeria

symbol email valeria.franceschi@univr.it symbol phone-number +39 045802 8729

Gaudenzi Barbara

symbol email barbara.gaudenzi@univr.it symbol phone-number 045 802 8623

Gnoatto Alessandro

symbol email alessandro.gnoatto@univr.it symbol phone-number 045 802 8537

Grossi Luigi

symbol email luigi.grossi@univr.it symbol phone-number 045 802 8247

Lai Alessandro

symbol email alessandro.lai@univr.it symbol phone-number 045 802 8574

Levati Maria Vittoria

symbol email vittoria.levati@univr.it symbol phone-number 045 802 8640
foto,  June 25, 2020

Magazzini Laura

symbol email laura.magazzini@univr.it symbol phone-number 045 8028525

Mancini Cecilia

symbol email cecilia.mancini@univr.it
Elena Manzoni,  February 4, 2020

Manzoni Elena

symbol email elena.manzoni@univr.it symbol phone-number 8783

Menon Martina

symbol email martina.menon@univr.it

Minozzo Marco

symbol email marco.minozzo@univr.it symbol phone-number 045 802 8234

Mola Lapo

symbol email lapo.mola@univr.it symbol phone-number 0458028565

Nardi Chiara

symbol email chiara.nardi@univr.it symbol phone-number +39 045 8028768

Pellegrini Letizia

symbol email letizia.pellegrini@univr.it symbol phone-number 045 802 8345

Perali Federico

symbol email federico.perali@univr.it symbol phone-number 045 802 8486

Peretti Alberto

symbol email alberto.peretti@univr.it symbol phone-number 0444 393936 (VI) 045 802 8238 (VR)

Pertile Paolo

symbol email paolo.pertile@univr.it symbol phone-number 045 802 8438

Picarelli Athena

symbol email athena.picarelli@univr.it symbol phone-number 045 8028242

Piovesan Marco

symbol email marco.piovesan@univr.it symbol phone-number 045.80.28.104

Quercia Simone

symbol email simone.quercia@univr.it symbol phone-number 045 802 8237

Renò Roberto

symbol email roberto.reno@univr.it symbol phone-number 045 802 8526

Ricciuti Roberto

symbol email roberto.ricciuti@univr.it symbol phone-number 0458028417

Rossi Francesca

symbol email francesca.rossi_02@univr.it symbol phone-number 045 802 8098

Rossignoli Cecilia

symbol email cecilia.rossignoli@univr.it symbol phone-number 045 802 8173

Scarpa Riccardo

symbol email riccardo.scarpa@univr.it

Scricciolo Catia

symbol email catia.scricciolo@univr.it symbol phone-number 045 8028341

Sommacal Alessandro

symbol email alessandro.sommacal@univr.it symbol phone-number 045 802 8716

Svaluto Ferro Sara

symbol email sara.svalutoferro@univr.it symbol phone-number 045 8028783

Veronesi Marcella

symbol email marcella.veronesi@univr.it

Zago Angelo

symbol email angelo.zago@univr.it symbol phone-number 045 802 8414

Zardini Alessandro

symbol email alessandro.zardini@univr.it symbol phone-number 045 802 8565

Zarri Luca

symbol email luca.zarri@univr.it symbol phone-number 045 802 8101

Zoli Claudio

symbol email claudio.zoli@univr.it symbol phone-number 045 802 8479

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