First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
MATHEMATICAL ENGINEERING
Course unit
STOCHASTIC DIFFERENTIAL EQUATIONS, WITH NUMERICS
INP5070418, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
MATHEMATICAL ENGINEERING (Ord. 2017)
IN2191, Degree course structure A.Y. 2017/18, A.Y. 2017/18
N0
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Degree course track FINANCIAL ENGINEERING [002PD]
Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination STOCHASTIC DIFFERENTIAL EQUATIONS, WITH NUMERICS
Department of reference Department of Civil, Environmental and Architectural Engineering
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge TIZIANO VARGIOLU MAT/06

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/06 Probability and Mathematical Statistics 9.0

Mode of delivery (when and how)
Period Second semester
Year 1st Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
teaching
Hours of
Individual study
Shifts
Lecture 9.0 72 153.0 No turn

Calendar
Start of activities 26/02/2018
End of activities 01/06/2018

Syllabus
Prerequisites: None
Target skills and knowledge: Objective
Introduce the students to the fundamental topics of stochastic differential equations and their numerical solution.
Outcomes
A student who has met the objectives of the course will have a basic knowledge of :
• Stochastic differential equations
• Monte Carlo simulations
Examination methods: Final examination based on: Written and oral examination.
Assessment criteria: Critical knowledge of the course topics. Ability to present the studied material.
Course unit contents: 1. Introduction to martingales.
2. Brownian motion.
3. Ito's stochastic integral.
4. Ito's formula and Girsanov theorem.
5. Stochastic differential equations (Geometric Brownian motion, Ornstein-Uhlenbeck process, other).
6. Feynman-Kac's formula.
7. Monte Carlo simulation of SDEs.
Planned learning activities and teaching methods: Lecture supported by tutorial, exercises and laboratory activities.
Additional notes about suggested reading: Lecture notes and reference books will be given by the lecturer.
Textbooks (and optional supplementary readings)