  Optimal multi-asset trading with Markovian predictors is well understood in
the case of quadratic transaction costs, but remains intractable when these
costs are $L_1$. We present a mean-field approach that reduces the multi-asset
problem to a single-asset problem, with an effective predictor that includes a
risk averse component. We obtain a simple approximate solution in the case of
Ornstein-Uhlenbeck predictors and maximum position constraints. The optimal
strategy is of the "bang-bang" type similar to that obtained in [de Lataillade
et al., 2012]. When the risk aversion parameter is small, we find that the
trading threshold is an affine function of the instantaneous global position,
with a slope coefficient that we compute exactly. We relate the risk aversion
parameter to the desired target risk and provide numerical simulations that
support our analytical results.
