  We consider the discretized Bachelier model where hedging is done on an
equidistant set of times. Exponential utility indifference prices are studied
for path-dependent European options and we compute their non-trivial scaling
limit for a large number of trading times $n$ and when risk aversion is scaled
like $n\ell$ for some constant $\ell>0$. Our analysis is purely probabilistic.
We first use a duality argument to transform the problem into an optimal drift
control problem with a penalty term. We further use martingale techniques and
strong invariance principles and get that the limiting problem takes the form
of a volatility control problem.
