  We consider a backward stochastic differential equation with jumps (BSDEJ)
which is driven by a Brownian motion and a Poisson random measure. We present
two candidate-approximations to this BSDEJ and we prove that the solution of
each candidate- approximation converges to the solution of the original BSDEJ
in a space which we specify. We use this result to investigate in further
detail the consequences of the choice of the model to (partial) hedging in
incomplete markets in finance. As an application, we consider models in which
the small variations in the price dynamics are modeled with a Poisson random
measure with infinite activity and models in which these small variations are
modeled with a Brownian motion. Using the convergence results on BSDEJs, we
show that quadratic hedging strategies are robust towards the choice of the
model and we derive an estimation of the model risk.
