Topic: An Introduction to Stochastic Differential Equations (with Applications to Mathematical Finance and Engineering)
The aim of this course is to provide a rigorous introduction to the theory of stochastic calculus and stochastic differential equations, and to survey some of its most important applications, especially in Mathematical Finance. The Ito stochastic integral and its associated Ito Calculus will be derived in the general framework of continuous semimartingales, leading to a detailed treatment of stochastic differential equations (SDEs) and their properties. The theory thus developed will be applied to selected problems in Mathematical Finance (option pricing and hedging, trading strategies and arbitrage) and Engineering (boundary-value problems, filtering, optimal control). Numerical aspects of SDEs will also be discussed.
(Lec: 3, Lab: 0, Tut: 0.5)