- Docente: Daniele Ritelli
- Credits: 8
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Financial Markets and Institutions (cod. 0901)
Learning outcomes
Mathematical tools in measure theory and differential equations in view of applications in Mathematical finance
Course contents
Lebesgue measure and Lebesgue integral. Abstract measure.
Probability measure. Beppo Levi's Theorem (monotone convergence),
Fatou's Lemma, dominated convergence Theorem. Derivation of
integrals dependent by a parameter. Integration in product spaces:
Fubini's Theorem. Decomposition of integrals on R^2. Change of
variable. Applications to the two dimensional random variables.
Absolute continuity: Radon-Nikodym Theorem. Lebesgue Stieltjes
measure. Review of some useful special functions: Euler Gamma and
Beta. Probability integral. Ordinary differential equations of
first order: linear and separable. Second order linear differential
equations. Partial differential equations: the heat equation
integrated by means of Fourier transform. Constant coefficients
Parabolic equations.
Readings/Bibliography
W. Rudin: Principles of Mathematical Analysis. Chap. 10. Mac Graw
Hill 1986
B. Osgood: The Fourier Transform and its Applications.
http://arni.epfl.ch/_media/courses/circuitsandsystems2011/book-2009.pdf
H. Hsu: Probability, Random Variables and Random Processes,
MacGraw Hill
F. Coppex: Solving the Black-Scholes equation: a
demystification. www.francoiscoppex.com/blackscholes.pdf
Teaching methods
Lessons ex Cathedra. Homework
Assessment methods
Written examination of 2 hours, where is possible to use calculators and self made formularies. The aim of the exam is to detect the capability of the student to face both theoretical and practical problems in the branch Mathematical Analysis which is useful in Finance.
Teaching tools
Video beamer. Blackboard.
Links to further information
http://www.danieleritelli.name
Office hours
See the website of Daniele Ritelli