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Course: 2022/2023

Advanced Stochastic Processes

(14472)

Bachelor in Statistics and Business (Plan: 400 - Estudio: 203)

Coordinating teacher: MEILAN VILA, ANDREA

Department assigned to the subject: Statistics Department

Type: Electives

ECTS Credits: 6.0 ECTS

Course: 4º

Semester:

Requirements (Subjects that are assumed to be known)

Stochastic Processes

Skills and learning outcomes

Link to document

Description of contents: programme

1 - Brownian motion 1.1 Definition and properties 1.2 Derived Processes 1.3 Simulation 2 - Martingales in continuous time 2.1 Definition and properties 2.2 Optional sampling theorem 3 - Stochastic Integration 3.1 Definition and properties 3.2 Lema of Itô 3.3 Girsanov's theorem 3.4 Martingale Representation Theorem 4 - Introduction to differential stochastic equations 4.1 Itô's Stochastic Differential Equations 4.2 Linear Differential Equations 4.3 Digital solutions 5 - Applications of stochastic calculus to Finance 5.1 The Black-Scholes formula 5.2 Risk neutral measures 5.3 Pricing Exotic options 5.4 Pricing American options

Learning activities and methodology

Theory (4 ECTS). Lectures. Practice (2 ECTS). Problem solving lessons.

Assessment System

The subject will be evaluated through the completion of exercises throughout the course and a final delivery of a work

% end-of-term-examination 0
% of continuous assessment (assigments, laboratory, practicals...) 100

Calendar of Continuous assessment

Basic Bibliography

H. Bühlmann. Mathematical Methods in Risk Theory.. Springer. 1996 (2nd. ed)
R. Durrett. Essentials of stochastic processes. Springer. 2012 (2nd ed.)
S. Asmussen and H. Albrecher. Ruin Probabilities. World Scientific. 2010 (2nd. ed.)
S.M. Ross. Stochastic Processes. John Wiley & Sons, inc.. 1996 (2nd. ed.)

Electronic Resources *

R. Durrett · Essentials of Stochastic Processes : http://www.math.duke.edu/~rtd/EOSP/EOSP2E.pdf

(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN

The course syllabus may change due academic events or other reasons.