PROBABILITY AND STOCHASTIC PROCESSES
Stampa
Enrollment year
2016/2017
Academic year
2016/2017
Regulations
DM270
Academic discipline
MAT/06 (PROBABILITY AND MATHEMATICAL STATISTICS)
Department
DEPARTMENT OF ECONOMICS AND MANAGEMENT
Course
ECONOMICS, FINANCE AND INTERNATIONAL INTEGRATION
Curriculum
Finance
Year of study
Period
1st semester (26/09/2016 - 22/12/2016)
ECTS
9
Lesson hours
66 lesson hours
Language
ENGLISH
Activity type
WRITTEN TEST
Teacher
LIJOI ANTONIO (titolare) - 9 ECTS
Prerequisites
The course is self-contained and no specific prerequisite is needed. Nonetheless, familiarity with the basic concepts in Probability typically taught in an introductory course in Statistics will be helpful.
Learning outcomes
This is a first course on Probability and Stochastic Processes, having economic and financial applications in view. Accordingly, after introducing some basic notions of probability theory (including conditional expectation), lectures will focus on those processes which are popular in finance, including martingales, Markov chains and Brownian motion. As far as possible, technicalities are avoided. Various exercises will be discussed as well.
Course contents
- Random variables and vectors
- Distribution functions
- Transformations of random variables and vectors
- Simulation of random variables
- Moment generating function
- Laws of large numbers
- Central limit theorem
- Conditional expectation
- Martingales
- Stopping times
- Brownian motion
Teaching methods
All lectures are displayed on the blackboard. Students are introduced to main theoretical concepts and results through a number of examples and illustrations that considerably ease the understanding of the subject.
Reccomended or required readings
* Billingsley P. (1995). "Probability and Measure". Wiley, 3rd Edition.
* Durrett, R. (2009). "Elementary Probability for Applications". Cambridge University Press.
* Resnick, S. (1998). "A Probability Path". Birkhaeuser.
Assessment methods
Oral
Further information
Oral
Sustainable development goals - Agenda 2030