Training and Research
PhD Programme Courses/classes
Mathematical Statistics
Credits: 5
Language: English
Teacher: Catia Scricciolo
Microeconomics 1
Credits: 7.5
Language: English
Teacher: Simona Fiore, Claudio Zoli, Martina Menon
Continuous Time Econometrics
Credits: 5
Language: English
Teacher: Cecilia Mancini
Probability
Credits: 7.5
Language: English
Teacher: Marco Minozzo
Macroeconomics I
Credits: 7.5
Language: English
Teacher: Tamara Fioroni, Alessia Campolmi
Game Theory
Credits: 5
Language: English
Teacher: Francesco De Sinopoli
Mathematics
Credits: 4.5
Language: English
Teacher: Andrea Mazzon, Jonathan Yick Yeung Tam
Advice to Young Economists
Credits: 4
Language: English
Teacher: Marco Piovesan
Stochastic Optimization and Control
Credits: 5
Language: English
Teacher: Athena Picarelli
Financial Time Series
Credits: 5
Language: English
Teacher: Giuseppe Buccheri, Francesca Rossi
Mean Field Games (part I)
Credits: 2.5
Language: English
Teacher: Luciano Campi
Job Market Orientation
Credits: 1
Language: English
Teacher: Joan Madia, Simone Quercia
Discretization of Processes
Credits: 4.5
Language: English
Teacher: Jean Jacod
Topics in applied economics with administrative data
Credits: 1
Language: English
Teacher: Edoardo Di Porto
Multivariate Analysis with Latent Variables: The SEM Approach
Credits: 3
Language: English
Teacher: Albert Satorra
Finanza Matematica
Credits: 5
Language: English
Teacher: Alessandro Gnoatto
Political Economy
Credits: 4
Language: English
Teacher: Emanuele Bracco, Roberto Ricciuti
Finite Mixture Models in Health Economics: Theory and Applications
Credits: 1
Language: English
Teacher: Paolo Li Donni
Inequality
Credits: 4
Language: English
Teacher: Francesco Andreoli, Claudio Zoli
Behavioral and Experimental Economics
Credits: 4
Language: English
Teacher: Simone Quercia, Maria Vittoria Levati, Marco Piovesan
Health Economics
Credits: 4
Language: English
Teacher: Paolo Pertile
Development economics
Credits: 4
Language: English
Teacher: Federico Perali
Finance
Credits: 4
Language: English
Teacher: Giorgio Vocalelli
Mean Field Games (part II)
Credits: 2.5
Language: English
Teacher: Giulia Liveri
Stochastic Processes in Finance
Credits: 5
Language: English
Teacher: Sara Svaluto-Ferro, Christa Cuchiero
Dynamic Corporate Finance
Credits: 2
Language: Englìsh
Probability (2023/2024)
Teacher
Referent
Credits
7.5
Language
English
Class attendance
Free Choice
Location
VERONA
Learning objectives
The course is intended for 1st year students on PhD in Economics and Finance.
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.
Prerequisites and basic notions
Basic Calculus and basic knowledge of probability theory. In particular, students should have been exposed to the material in Lectures 1, 2, 3, 4, 5, 6, 8 of the MIT online course “Introduction to Probability” (RES.6-012) by John Tsitsiklis and Patrick Jaillet
https://ocw.mit.edu/courses/res-6-012-introduction-to-probability-spring-2018/
Attendance to more advanced courses such as real analysis, probability, distribution theory and statistical inference would be desirable.
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.
Bibliography
Didactic methods
The lesson will be delivered in presence. Topics will be illustrated with the use of many examples.
Learning assessment procedures
A two-hour written paper at the end of the course. No material is permitted during the examination.
Scheduled Lessons
| When | Classroom | Teacher | topics |
|---|---|---|---|
|
Wednesday 04 October 2023 14:00 - 17:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Marco Minozzo | Probability |
|
Friday 06 October 2023 09:00 - 12:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Marco Minozzo | Probability |
|
Wednesday 18 October 2023 14:00 - 17:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Marco Minozzo | Probability |
|
Wednesday 25 October 2023 14:00 - 17:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Marco Minozzo | Probability |
|
Wednesday 08 November 2023 14:00 - 17:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Marco Minozzo | Probability |
|
Monday 13 November 2023 09:00 - 12:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Marco Minozzo | Probability |
|
Tuesday 14 November 2023 09:00 - 12:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Marco Minozzo | Probability |
|
Wednesday 15 November 2023 14:00 - 17:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Marco Minozzo | Probability |
|
Wednesday 22 November 2023 14:00 - 17:00 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Marco Minozzo | Probability |
|
Wednesday 29 November 2023 14:00 - 17:00 Duration: 2:50 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Marco Minozzo | Probability |
|
Friday 12 January 2024 15:00 - 18:00 Duration: 12:10 AM |
Polo Santa Marta - SMT.07 [SMT.7 - terra] | Marco Minozzo | EXAM: Probability |
