Executing a basket of co-integrated assets is an important task facing investors. Here, we show how to do this accounting for the informational advantage gained from assets within and outside the basket, as well as for the permanent price impact of market orders (MOs) from all market participants, and the temporary impact that the agent's MOs have on prices. The execution problem is posed as an optimal stochastic control problem and we demonstrate that, under some mild conditions, the value function admits a closed-form solution, and prove a verification theorem. Furthermore, we use data of five stocks traded in the Nasdaq exchange to estimate the model parameters and use simulations to illustrate the performance of the strategy. As an example, the agent liquidates a portfolio consisting of shares in Intel Corporation and Market Vectors Semiconductor ETF. We show that including the information provided by three additional assets (FARO Technologies, NetApp, Oracle Corporation) considerably improves the strategy's performance; for the portfolio we execute, it outperforms the multiasset version of Almgren-Chriss by approximately 4-4.5 basis points. K E Y W O R D Salgorithmic trading, co-integration, co-movements, cross-price impact, optimal execution, price impact 542

We consider an agent who takes a short position in a contingent claim and employs limit orders (LOs) and market orders (MOs) to trade in the underlying asset to maximize expected utility of terminal wealth. The agent solves a combined optimal stopping and control problem where trading has frictions: MOs (executed by the agent and other traders) have permanent price impact and pay exchange fees, and LOs earn the spread (relative to the midprice of the asset) and pay no exchange fees. We show how the agent replicates the payoff of the claim and also speculates in the asset to maximize expected utility of terminal wealth. In the strategy, MOs are used to keep the inventory on target, to replicate the payoff, and LOs are employed to build the inventory at favorable prices and boost expected terminal wealth by executing roundtrip trades that earn the spread. We calibrate the model to the E-mini contract that tracks the S\&P 500 index, provide numerical examples of the performance of the strategy, and prove that our scheme converges to the viscosity solution of the dynamic programming equation.

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We show how the position of a limit order in the queue influences the decision of whether to cancel the order or let it rest. Using ultra high-frequency data from the Nasdaq exchange, we perform empirical analysis on various limit order book events and propose novel ways for modelling some of these events, including cancellation of limit orders in various positions and size of market orders. Based on our empirical findings, we develop a queuing model that captures stylized facts on the data. This model includes a distinct feature which allows for a potentially random effect due to the agent's impulse control. We apply the queuing model in an algorithmic trading setting by considering an agent maximizing her expected utility through placing and cancelling of limit orders. The agent's optimal strategy is presented after calibrating the model to real data. A simulation study shows that for the same level of standard deviation of terminal wealth, the optimal strategy has a 2.5% higher mean compared to a strategy which ignores the effect of position; or a 8.8% lower standard deviation for the same level of mean. This extra gain stems from posting a limit order during adverse conditions and obtaining a good queue position before conditions become favourable.

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