  Trading frictions are stochastic. They are, moreover, in many instances
fast-mean reverting. Here, we study how to optimally trade in a market with
stochastic price impact and study approximations to the resulting optimal
control problem using singular perturbation methods. We prove, by constructing
sub- and super-solutions, that the approximations are accurate to the specified
order. Finally, we perform some numerical experiments to illustrate the effect
that stochastic trading frictions have on optimal trading.
