This dissertation addresses two different problems within mathematical finance: an optimal execution problem with dark pools using a market impact model, and multi-product separation with financial hedging for inventory management. In the first part of the dissertation we consider an optimal liquidation problem in which a large investor can sell on a traditional exchange or in a so-called dark pool. Dark pools differ from traditional exchanges in that the orders placed in it generate little to no price impact on the market price of the asset. Within the framework of the Almgren-Chriss market impact model, we study an extended model which includes the cross-impact between the two venues. By analyzing the optimal execution strategy, we identify those model specifications for which the corresponding order execution problem is stable in the sense that are no price manipulation strategies which can be beneficial. In the second part of the dissertation, we propose financial hedging tools for inventory management. Based on a framework for hedging against the correlation of operational returns with financial market returns, we consider the general problem of optimizing simultaneously over both the operational policy and the hedging policy of the corporation. Our main goal is to achieve a separation result such that for a corporation with multiple products and inventory departments, the inventory decisions of each department can be made independently of the other departments' decisions. We focus initially on a single-period, multi-product hedging problem for inventory management, and model an economy experiencing monetary inflation. We use the Heath-Jarrow- Morton model to represent the financial market. We then extend the model to consider multiple periods and more general market models. In both cases, we prove a separation result for inventory management that allows each inventory department to make decisions independently. In particular, the separation result for the multi-period problem is a global separation in the sense that no interaction needs to be considered among products in intermediate time periods. In addition, we propose a dynamic programming simplification of the multi-period single-item inventory problem which further simplifies the computation by reducing the dimension of the state space.