### Abstract or Additional Information

**Abstract:** We consider an optimal execution problem in which the agent has exposure to an untraded risk factor but where the agent is allowed to trade in an asset which is correlated with the risk factor. In a similar fashion to previous work, we account for the possibility of price impact, both permanent and temporary, due to the agent's trades. We also include a feature which accounts for the impact that the agent's trades will have on the value of the untraded risk factor, deemed cross price impact. In the case where the agent holds shares of an untraded asset (linear exposure) we solve in closed form for the optimal trading strategy. When the exposure held by the agent has non-linear dependence on the untraded risk factor we solve in closed form for an approximation of the optimal trading strategy which applies when cross price impact and risk-aversion are small.