Stochastic Differential Equations

This seminar was given 13 May 2009 as part of the PhD seminar series organised by the School of Economics & Finance of the University of St Andrews.

Dr Evelyn Buckwar speaks about stochastic differential equations. Starting from ordinary differential equations, she discusses Brownian motion and how it can be used to include the aspect of uncertainty in a continuous time dynamic framework. She emphasizes the point on how one deals with stochastic differential equations numerically, how to simulate paths, how to use them to compute the price of an option via Monte Carlo simulation for example, but also discuss applications in Economics, such as the stochastic Solow model and from Biology, in particular Population dynamics.

Videos are in MP4 format. Handouts are PDF.

Due to technical difficulties on the day, we do not have the video of the first session in the morning.

Morning video 2 (30 minutes) - Dr Buckwar devotes the second part of her morning session to Stratonovich integral and the Stratonovich Stochastic Differential Equations (SDEs) Download MP4 | (slides 28 - 39)

Afternoon video 1 (50 minutes) - In her afternoon session, Dr Buckwar presents a series of ordinary differential equations. She explains various numerical methods to solve them and tackles the convergence issues. Download MP4 | (slides 1 - 30)

Afternoon video 2 (27 minutes) - Dr Buckwar concludes her lectures by focusing on stability behaviour of these equations. Download MP4 | (slides 31 - 39)

About the Speaker

Dr Buckwar is Lecturer in the Department of Mathematics at Heriot-Watt University (UK). Her research interests focus on the analysis and numerical analysis of stochastic differential equations with and without memory terms, as well as applications in neuroscience, population dynamics and finance.