Mathematics for Finance (9cfu-63 hours)

Instructors: Paolo Ghirardato and Bertrand Lods

NEWS:

• RESULTS OF THE FINAL EXAM are available. Please email Prof. Ghirardato to be told yours.

• PAOLO GHIRARDATO'S OFFICE HOURS: For the next months, Prof. Ghirardato is available to meet students (in his office in the Dipartimento) on the following days:

  • FRIDAYS, 8:45-10:15

  However, such office hours are secured by email appointment: if you want to meet with him on a specific Friday, please send an email (no later than the previous morning) by clicking here.

  He is also available at other times, also by email appointment.

• BERTRAND LODS' OFFICE HOURS: During the Fall semester Prof. Lods will see students (in his office in the former Department of Statistics and Applied Mathematics) on gthe following days:

  • time to be announced

  Prof. Lods is also available by appointment. Send him an email by clicking here.

SYLLABUS: This is an introductory course to the Theory of Probability and Stochastic Processes, with emphasis on their applications to investment and insurance decisions.

The course is divided in two parts:

Part 1: Measure, Probability and basics of decision making (Ghirardato and Lods)

• Foundations of measure theory. Measures, measurable functions, Lebesgue integrals, Lp spaces, theorems of Fubini (if time allows) and Radon-Nikodym
• Applications of measure theory to probability calculus. Conditional probabilities and expectation, filtrations

• Martingales and their convergence
• Markov chains (if time allows)
• The Poisson process: construction and properties. Some examples
• Probability measures on real-valued function spaces. The Wiener measure
• Brownian motion: construction and properties. Variation in Brownian motion

• M. Capinski e E. Kopp, Measure, Integral and Probability, Second Edition, Springer-Verlag, Berlino, 2005. (Chapters 1-7 (except 7.3))
• Z. Brzezniak and T. Zastawniak, Basic Stochastic Processes, Springer-Verlag, Berlino, 1999. (Chapters 1-4 and 6-7)

EXERCISES: The following exercises are very important as practice and verification of your understanding of the course material:

• Homework 1, with Solutions
• Homework 2
• Homework 3
• Homework 4

PAST EXAMS: These are some past exams of this course (please, be warned that these exams are for the 84-hour version of the course, so they cover material -in particular Ito calculus- that is not currently covered):

• December 2009
• January 2010
• February 2010
• January 2011
• February 2011

CONTACTS
paolo.ghirardato at unito.it
bertrand.lod at unito.it

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