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

Credits

5

Language

English

Class attendance

Free Choice

Location

VERONA

Learning objectives

The course presents the main techniques of stochastic optimal control in continuous time and its applications in finance.

Prerequisites and basic notions

Stochastic calculus, ordinary and partial differential equations. Basics of numerical analysis.

Program

Introduction to stochastic optimal control in continuous time;
Maximum Principle;
Dynamic Programming Principle;
Optimal Control and backward stochastic differential equations;
Numerical approximation;
Free boundary problems, constrained problems.

Bibliography

Visualizza la bibliografia con Leganto, strumento che il Sistema Bibliotecario mette a disposizione per recuperare i testi in programma d'esame in modo semplice e innovativo.

Didactic methods

Lectures

Learning assessment procedures

Written test

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

Assessment

It will be evaluated the ability of the student to apply the presented techniques to solve optimal control problems.

Criteria for the composition of the final grade

Obtained mark in the written test

Scheduled Lessons

When Classroom Teacher topics
Monday 15 January 2024
15:00 - 17:00
Duration: 2:00 AM
Polo Santa Marta - SMT.07 [SMT.7 - terra] Athena Picarelli Introduction to stochastic control: from calculus of variations and deterministic optimal control to the stochastic case. Definition of value function and optimal control. Example: Merton portfolio selection problem.
Monday 22 January 2024
15:00 - 18:00
Duration: 3:00 AM
Polo Santa Marta - SMT.07 [SMT.7 - terra] Athena Picarelli The Pontryagin Maximum Principle. Sketch of the proof. Introduction to backward stochastic differential equations.
Thursday 25 January 2024
15:00 - 18:00
Duration: 3:00 AM
Polo Santa Marta - SMT.07 [SMT.7 - terra] Athena Picarelli The Dynamic Programming Principle. Sketch of the proof. Formal derivation of the Hamilton-Jacobi-Bellman equation. Example of non smooth value function.
Thursday 15 February 2024
15:00 - 17:00
Duration: 2:00 AM
Polo Santa Marta - SMT.07 [SMT.7 - terra] Athena Picarelli Viscosity solutions to HJB equation and comparison principle.
Monday 19 February 2024
15:00 - 17:00
Duration: 2:00 AM
Polo Santa Marta - SMT.07 [SMT.7 - terra] Athena Picarelli Other optimal control problems: infinite horizon problems and optimal stopping problems
Thursday 22 February 2024
15:30 - 17:00
Duration: 1:30 AM
Polo Santa Marta - SMT.07 [SMT.7 - terra] Athena Picarelli Optimal control problems with exit time and state constrained problems
Monday 26 February 2024
14:30 - 17:00
Duration: 2:30 AM
Polo Santa Marta - SMT.07 [SMT.7 - terra] Athena Picarelli Impulsive optimal control problems and optimal switching. An overview on the link between optimal control and BSDEs: Pntryagin, Dynamic Programming, weak formulation. Martingale method for utility maximization problems.
Thursday 29 February 2024
15:00 - 17:00
Duration: 2:00 AM
Polo Santa Marta - Sala Andrea Vaona (DSE) [1.59 - 1] Athena Picarelli Massimizzazione di utilità attesa attraverso il metodo martingala. Soluzione numerica di problemi di controllo stocastico: introduzione.
Thursday 07 March 2024
14:00 - 16:00
Duration: 2:00 AM
Polo Santa Marta - Sala Andrea Vaona (DSE) [1.59 - 1] Athena Picarelli Metodi numerici: monotonia, stabilità, consistenza. Convergenza all'unica soluzione di viscosità dell'equazione HJB. Metodi semi-Lagrangiani.