Checking date: 24/05/2022

Course: 2022/2023

Advanced Stochastic Processes
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


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