  We consider the problem of hedging a European contingent claim in a Bachelier
model with transient price impact as proposed by Almgren and Chriss. Following
the approach of Rogers and Singh and Naujokat and Westray, the hedging problem
can be regarded as a cost optimal tracking problem of the frictionless hedging
strategy. We solve this problem explicitly for general predictable target
hedging strategies. It turns out that, rather than towards the current target
position, the optimal policy trades towards a weighted average of expected
future target positions. This generalizes an observation of Garleanu and
Pedersen from their homogenous Markovian optimal investment problem to a
general hedging problem. Our findings complement a number of previous studies
in the literature on optimal strategies in illiquid markets where the
frictionless strategy is confined to diffusions. The consideration of general
predictable reference strategies is made possible by the use of a convex
analysis approach instead of the more common dynamic programming methods.
