Numerical Methods for SDEs in Mathematical Finance

Michaela Szoelgyenyi (Vienna University of Economics and Business)
Thursday, May 18, 2017 - 5:00pm
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 043

When solving certain stochastic control problems in insurance mathematics or mathematical finance, the optimal control policy sometimes turns out to be of threshold type, meaning that the control depends on the controlled process in a discontinuous way. The stochastic differential equations (SDEs) modeling the underlying process then typically have a discontinuous drift coefficient. This motivates the study of a more general class of such SDEs.
We prove an existence and uniqueness result, based on a certain transformation of the state space by which the drift is "made continuous". As a consequence the transform becomes useful for the construction of a numerical method. The resulting scheme is proven to converge with strong order 1/2. This is the first scheme for which strong convergence is proven for such a general class of SDEs with discontinuous drift.
As a next step, the transformation method is applied to prove strong convergence with positive rate of the Euler-Maruyama scheme for this class of SDEs.
Joint work with G. Leobacher (University of Graz).