| CODE | 109055 |
|---|---|
| ACADEMIC YEAR | 2022/2023 |
| CREDITS |
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| SCIENTIFIC DISCIPLINARY SECTOR | MAT/06 |
| TEACHING LOCATION |
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| SEMESTER | 2° Semester |
| TEACHING MATERIALS | AULAWEB |
The course introducts stochastic calculus and martingale theory, that naturally intervene in applications in economics.
Introduction to Stochastic Calculus and Martingale Theory. Applications in finance.
Upon completion of the course, the student knows the fundamentals of the theory of stochastic processes in discrete and continuous time; he also learns the mathematical basis of stochastic calculus according to Itô. He/she is able to handle advanced tools of probability and stochastic process theory and sees some applications to the financial world.
Probability Theory
Letures.
Conditional Expectation/filtrations and stopping times/discrete-time martingale (Doob's inequalities, convergence results; Doob-Meyer decomposition)/continuous-time martingale (Continuous or continuous right-handed trajectory versions with limits from the left. Kolmogorov's theorem. Continuous-time martingales and their properties. Martingales closed by an integrable or integrable square random variable)
Brownian motion (scale change invariance property, strong Markov property, reflection principle, law of maximum, level crossing times, geometric Brownian motion, multidimensional Brownian motion, recurrence and transience. Brownian motion with drift. Ornstein-Uhlenbeck process, Bessel process, Brownian bridge.)/ Stochastic integration/Simulation MB/ Applications to finance.
A. Pascucci, PDE and Martingale methods in Option Pricing, Bocconi & Springer Series (2010)
P. Baldi, S. Shreve, Stochastic Calculus and Finance
P. Baldi, Equazioni differenziali stocastiche e applicazioni, Bologna, Pitagora (2000)
Mörters, Peres, Brownian Motion
F. Caravenna, Moto browniano e analisi stocastica
Office hours: By appointment by email.
Office hours: By appointment by email.
VERONICA UMANITA' (President)
EMANUELA SASSO
The class will start according to the academic calendar.
All class schedules are posted on the EasyAcademy portal.
Oral test.
Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.
Verification of learning is by oral examination only and will focus on topics covered in class. The student will be expected to show correctness in mathematical language and formalism, be well acquainted with the mathematical objects and results of the course, and be able to use them naturally.