Adaptive basket liquidation

We consider the infinite time-horizon optimal basket portfolio liquidation problem for a von NeumannMorgenstern investor in a multi-asset extension of the liquidity model of Almgren (2003) with cross-asset impact. Using a stochastic control approach, we establish a “separation theorem”: the sequence of portfolios held during an optimal liquidation depends only on the (co-)variance and (cross-asset) market impact of the assets, while the speed with which these portfolios are attained depends only on the utility function of the trader. We derive partial differential equations for both the sequence of attained portfolios and the trading speed.