Training and Research
PhD Programme Courses/classes
This page lists the training activities for the PhD programme for the academic year 2025/2026. Additional activities will be added during the year. Please check back regularly for updates!
Mathematics
Credits: 7.5
Language: English
Teacher: Corrado De Vecchi, Andrea Mazzon
Probability
Credits: 7.5
Language: English
Teacher: Marco Minozzo
Introduction to Economics
Credits: 5
Language: English
Teacher: Roberto Ricciuti
Mathematical Statistics
Credits: 5
Language: English
Teacher: Catia Scricciolo
Continuous Time Econometrics
Credits: 5
Language: English
Teacher: Cecilia Mancini
Macroeconomics I
Credits: 7.5
Language: INGLESE
Teacher: Tamara Fioroni, Alessia Campolmi
Microeconomics I
Credits: 10.5
Language: English
Teacher: Simona Fiore, Claudio Zoli, Martina Menon
Game Theory
Credits: 5
Language: English
Teacher: Francesco De Sinopoli
Financial Time Series
Credits: 5
Language: English
Teacher: Giuseppe Buccheri, Lorenzo Frattarolo
Stochastic Optimization and Control
Credits: 5
Language: English
Teacher: Athena Picarelli
Advice to Young Researchers
Credits: 4
Language: English
Teacher: Marco Piovesan
Job Market Orientation
Credits: 2
Language: English
Teacher: Simone Quercia
Behavioral and Experimental Economics
Credits: 4
Language: English
Teacher: Simone Quercia, Maria Vittoria Levati, Marco Piovesan
Inequality
Credits: 4
Language: English
Teacher: Francesco Andreoli, Claudio Zoli, Lidia Ceriani
Development Economics
Credits: 4
Language: Italian
Teacher: Federico Perali
Health Economics
Credits: 4
Language: English
Teacher: Paolo Pertile, Paola Bertoli
Stochastic Processes in Finance
Credits: 5
Language: English
Teacher: Sara Svaluto-Ferro
Political Economy
Credits: 4
Language: English
Teacher: Emanuele Bracco, Roberto Ricciuti
Financial Mathematics
Credits: 5
Language: Inglese
Teacher: Alessandro Gnoatto
Continuous Time Econometrics (2025/2026)
Teacher
Referent
Credits
5
Language
English
Class attendance
Compulsory
Location
VERONA
Learning objectives
The course aims to introduce the class of semimartingale processes with jumps, used in the literature as financial asset price models, and to provide tools for estimating and testing jumps in financial asset prices
Prerequisites and basic notions
Basic probability, basic statistics, Brownian motion, Ito integral
Program
Poisson process, random measures and Poisson random measures
Semimartingales with jumps and Lévy processes
Semimartingale models for financial asset prices:
Brownian SM, finite activity jumps,
infinite activity jumps, pure jump models
Quadratic variation
Estimating the jumps given discrete observations
Testing for jumps
Bibliography
Didactic methods
Classroom lessons, assignments consisting of the study of the proof of some results to be told and commented on in class
Learning assessment procedures
Each student can choose either a written exam about one of the topics dealt with during the course, or an individual written and reasoned report deepening one of the topics proposed after the course
Assessment
Rigor, creativity, exposure
Criteria for the composition of the final grade
Rigor 4 points out of 10, creativity 3, exposure 3
Scheduled Lessons
| When | Classroom | Teacher | topics |
|---|---|---|---|
|
Wednesday 29 October 2025 09:30 - 12:30 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Cecilia Mancini | Stochastic models for financial asset prices: Brownian semimartingales. Motivations for introducing jump components: 1. visual inspection at specific time resolutions; 2. log-returns heavy tails; 3. short-term option prices. Aims of a model: 1. measuring risk; 2. derivative pricing; 3. hedging the risk. Semimartingales with jumps. The simplest jump tool: the Poisson process (PP). Problems associated with the presence of jumps: testing for jumps, estimating the model coefficients. Outline of the course. A first property of the PP: finiteness at each t. |
|
Wednesday 05 November 2025 09:30 - 12:30 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Cecilia Mancini | Properties of the PP: piecewise constant paths, cadlag paths, continuity in probability of the paths, no fixed time of discontinuity, probability that N_t=n. Proofs and comments |
|
Wednesday 12 November 2025 09:30 - 12:30 Duration: 3:00 AM |
Polo Santa Marta - Sala Andrea Vaona (DSE) [1.59 - 1] | Cecilia Mancini | The Poisson process: characteristic function, infinite divisibility, stationary and independent increments, Markov property. Proofs and comments. Lévy processes, examples, counting processes in general, finite/infinite activity jumps. |
|
Wednesday 19 November 2025 09:30 - 12:30 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Cecilia Mancini | Cadlag paths: finitely many jumps above a fixed threshold, countably many jumps, possibly dense. Compensated Poisson process, Compound Poisson process (CPP) and characteristic function, compensated CPP, Lévy measure, pure jump processes, jump frequency Rescaled PP as an approximation of the BM; PPs with different jump sizes as an approximation of the CPP; the CPP as an approximation of any Lévy process. |
|
Wednesday 26 November 2025 09:30 - 12:30 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Cecilia Mancini | The Lévy process as a prototypical example of Ito semimartingale (SM): comparison of the relative Ito and Grigelionis representations. Random measure associated with the PP, Radon measures, integrals with respect to a Radon measure. Illustration on how we obtain the result of an integral, examples. Random jump measure associated with any stochastic process with cadlag paths, representation with Dirac deltas, characterization of finite activity/infinite activity path, example of integrals, difference with the Ito integral |
|
Wednesday 10 December 2025 09:30 - 12:30 Duration: 3:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Cecilia Mancini | Adapted processes and financial meaning, finite variation processes, examples, crucial role of the small jumps in determining finite/infinite variation of a jump process. Alpha stable processes and finite variation, jump activity index, examples. When a process satisfies a certain property locally, stopping times, stopped process, predictable processes. Formal definition of compensator, existence of a compensator for counting processes. Compensating measures for a cadlag adapted counting process, examples. Integrals in the compensated jump measure of a cadlag adapted process: finite variation and infinite variation cases. Examples. Usefulness of the compensating measure in practice. Characteristic function of a Lévy process and the meaning of each component. Quadratic variation (QV) of an SM, examples of computation of QV. |
|
Wednesday 17 December 2025 09:30 - 12:30 Duration: 2:00 AM |
Polo Santa Marta - SMT.04 [SMT.4 - terra] | Cecilia Mancini | Use of QV in practice to measure the risk of a financial asset modeled by an Ito SM. Components of the QV, importance of disentangling if we have discrete observations of the SM. Relevant features of the paths of a Brownian SM. Detection of the intervals where the SM made a jump, Threshold Realized Variance (TRV), estimation of integrated volatility (IV, comments, extensions, central limit theorems for TRV. BiPower Variation: another method to estimate IV, test for jumps. How distant is an SM from an Ito SM? Formal definition of an SM, representation, characteristic triplet, special cases, examples, Poisson random measure, compensated Poisson random measure, and their usefulness in practice. |
