Stochastic Calculus

Duration

Two Weeks, Period 1 (followed by Financial Mathematics)

Lecturer

John van der Hoek (University of Adelaide)

Consultation Hour

Week 1: Tuesday 17–18h, Week 2: Wednesday 15–16h in Carslaw Room 633.

Assessment

take home exam to be posted to Dr John van der Hoek, School of Mathematical Sciences, The University of Adelaide, SA 5005 by date TBA.

Course Outline

• Probability preliminaries [including sigma algebras, filtrations and conditional expectations, martingales]
• Brownian motion and its characterrizations
• Ito integrals and related integrals
• Ito’s Lemma
• Stochastic Differential Equations
• Partial Differential Equations and Feynman-Kac formula
• Changes of Probability and Girsanov’s Theorem
• Martingale representation theorems