93013 - Stochastic Processes

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education Industry, innovation and infrastructure

Academic Year 2021/2022

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
  • Poisson process: definition and basic properties


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 3 exercises each with a maximum grade of 10 points. Every exercise attains to elements of the syllabus covered during the course lectures. Online exams 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