Stochastic Calculus

The aim of this course is the provide solid working knowledge of stochastic differential and stochastic calculus since stochastic differential equations are used to model the behaviour of financial assets and stochastic calculus is the fundamental tool for understanding and manipulating these models.

At the end of the course, participants should be able to solve different types of linear stochastic differential equations, understand and apply Ito’s Lemma for scalar and vector stochastic processes, understand the connection between stochastic differential equations and partial differential equation of the heat equation type and perform many of needed calculations using both pen and paper as well as using symbolic and numerical computations.

This course is elective. It is taught in the first semester and carries 6 ECTS credits. Go to the next course or see the list of courses.

  • Essential Literature
  • J. Cvitanić, F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, MIT Press (2004).
  • T. Mikosch, Elementary Stochastic Calculus with Finance in View, World Scientific (2008).