Checking date: 24/05/2022


Course: 2022/2023

Advanced Stochastic Processes
(14472)
Study: Bachelor in Statistics and Business (203)


Coordinating teacher: MEILAN VILA, ANDREA

Department assigned to the subject: Department of Statistics

Type: Electives
ECTS Credits: 6.0 ECTS

Course:
Semester:




Requirements (Subjects that are assumed to be known)
Stochastic Processes
Skills and learning outcomes
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
  • % 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.)
Recursos electrónicosElectronic Resources *
(*) 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.