Stochastics and Finance: Georg Gottwald -- Simulation of non-Lipschitz SDEs driven by alpha-stable noise: a method based on deterministic homogenisation

Dear All, 

You are kindly invited to attend the next Stochastic and Finance seminar.  On Tuesday
July 14 at 2pm (Sydney time) Georg Gottwald will give a talk via Zoom.  

Zoom link: https://uni-sydney.zoom.us/j/96667003785 

Speaker: Georg Gottwald (U Sydney) 

Title: Simulation of non-Lipschitz stochastic differential equations driven by
alpha-stable noise: a method based on deterministic homogenisation 

Abstract: The talk introduces an explicit method to integrate alpha-stable stochastic
differential equations (SDEs) with non-Lipschitz coefficients.  To mitigate against
numerical instabilities caused by unbounded increments of the Levy noise, we use a
deterministic map which has the desired SDE as its homogenised limit.  Moreover, our
method naturally overcomes difficulties in expressing the Marcus integral explicitly.
We present an example of an SDE with a natural boundary showing that our method respects
the boundary whereas Euler-Maruyama discretisation fails to do so.  As a by-product we
devise an entirely deterministic method to construct alpha-stable laws.  This is joint
work with Ian Melbourne.  

http://www.maths.usyd.edu.au/u/SemConf/Stochastics_Finance/seminar.html 

Kind regards, 

Anna