- Docente: Alberto Lanconelli
- Credits: 6
- SSD: MAT/06
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Quantitative Finance (cod. 8854)
-
from Nov 06, 2023 to Dec 12, 2023
Learning outcomes
Students will acquire new mathematical/probabilistic skills in the field of stochastic processes becoming more self-conscious in applying them to models of financial market and any pricing issues.
Course contents
- Brownian motion: definition and basic properties
- Ito integral: definition and key features
- Extension of the Ito integral and examples
- Ito's formula and applications
- Stochastic differential equations: existence, uniqueness and examples
- Numerical methods and simulation of stochastic differential equations
Readings/Bibliography
Lecture notes.
Suggested readings:
- H. H. Kuo, Introduction to Stochastic Integration, Springer, 2006
- B. Øksendal, Stochastic differential equations - VI edition, Springer, 2003
- R. L. Schilling and L. Partzsch, Brownian Motion. An Introduction to Stochastic Processes, De Gruyter, Berlin, 2012
Teaching methods
Regular lectures
Assessment methods
Written exam, articulated in a series of 2 exercises each with a maximum grade of 15 points. Every exercise attains to elements of the syllabus covered during the course lectures. In case of online exam, this will be supported by the softwares Teams, Zoom and EOL (https://eol.unibo.it/)
Teaching tools
Slides and exercises with solutions
Office hours
See the website of Alberto Lanconelli
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.