Mathematics for Finance

Instructors: Paolo Ghirardato and Bertrand Lods

NEWS:

EXAM GRADE TRANSCRIPTION (REGISTRAZIONE ESAME): Next exam grade transcriptio will take place Friday, March 16 at 9, in Prof. Ghirardato's office in the Dipartimento.
PAOLO GHIRARDATO'S OFFICE HOURS: Starting March 2012, Prof. Ghirardato will see students by appointment (send an email).
BERTRAND LODS' OFFICE HOURS: Starting March 2012, Prof. Lods will see students by appointment (send an email).

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)

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

Part 2: Stochastic Processes (Lods)

Martingales and their convergence
Markov chains
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
The Ito integral: definition and properties. The Ito formula for Brownian motion. Some examples
Stochastic differential equations (if time allows)
Diffusion processes and stochastic differential equations (if time allows)

The following are the required textbooks for the course:

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 1-5)

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

PAST EXAMS: These are some past exams of this course:

CONTACTS
ghirardato at econ.unito.it
lods at econ.unito.it

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Created: 09/10/09. Last revised: 14/03/12