This talk will discuss work-in-progress on the numerical approximation
of reflected diffusions arising from applications in engineering, finance
and network queueing models. Standard numerical treatments with
uniform timesteps lead to 1/2 order strong convergence, and hence
sub-optimal behaviour when using multilevel Monte Carlo (MLMC).
In simple applications, the MLMC variance can be improved by through
a reflection "trick". In more general multi-dimensional applications with
oblique reflections an alternative method uses adaptive timesteps, with
smaller timesteps when near the boundary. In both cases, numerical
results indicate that we obtain the optimal MLMC complexity.
This is based on joint research with Eike Muller, Rob Scheichl and Tony
Shardlow (Bath) and Kavita Ramanan (Brown).
- Mathematical Finance Internal Seminar