  Continuous time financial market models are often motivated as scaling limits
of discrete time models. The objective of this paper is to establish such a
connection for a robust framework. More specifically, we consider discrete time
models that are parameterized by Markovian transition kernels, and a continuous
time setting with drift and volatility uncertainty, again parameterized in a
Markovian way. Our main result shows convergence of the uncertainty sets in the
Hausdorff metric topology and weak convergence of the associated worst-case
expectations. Furthermore, we discuss a structure preservation property of the
approximation. Namely, we establish the convergence of discrete to continuous
time robust superhedging prices for certain complete robust market models. As
an application of our main convergence result, we derive a simple algorithm to
compute continuous time robust superhedging prices via approximation and
dynamic programming.
