  An investor trades a safe and several risky assets with linear price impact
to maximize expected utility from terminal wealth. In the limit for small
impact costs, we explicitly determine the optimal policy and welfare, in a
general Markovian setting allowing for stochastic market, cost, and preference
parameters. These results shed light on the general structure of the problem at
hand, and also unveil close connections to optimal execution problems and to
other market frictions such as proportional and fixed transaction costs.

Portfolio Management;Analysis of PDEs;Optimization and Control;Trading and Market Microstructure