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Advanced Probability Theory

  • Teacher(s):
  • Course given in: English
  • ECTS Credits:
  • Schedule: Spring Semester 2017-2018, 2.0h. course (weekly average)
      WARNING :   this is an old version of the syllabus, old versions contain   OBSOLETE   data.
  •  séances
  • Related programmes:

 

Objectives

This course builds upon Probability and Stochastic Processes course and provides an introduction to more advanced probabilistic techniques required to understand the most popular actuarial and financial models.

Contents

Reminder of basic concepts in probability theory

  • Probability space, Lebesque integral, change of measure, conditional expectation, etc

Stochastic processes

  • Brownian motion (BM), martingales, random walk, Lévy process

Stochastic calculus

  • Integrals with respect to BM, Itô-Doeblin formula, Girsanov's theorem, stochastic differential equations (SDE)

Financial applications

  • Black-Scholes model, stochastic interest rate models, pricing of options and bonds, risk neutral valuation, portfolio optimization

References

  • Stochastic Calculus for Finance II, S. Shreve
  • Introduction to Probability Models, S. M. Ross

Pre-requisites

Probability and Stochastic Processe ( see courses index )

Evaluation

First attempt

Exam:
Written 2h00 hours
Documentation:
Allowed with restrictions
Calculator:
Allowed with restrictions
Evaluation:

Exam 60% + class participation 20% + mid-term 20%

Retake

Exam:
Written 2h00 hours
Documentation:
Allowed with restrictions
Calculator:
Allowed with restrictions
Evaluation:

Retake exam 60% + class participation 20% + mid-term 20%



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