Traditional approaches to portfolio optimization, still widely used in practice, treat trading as frictionless and the parameters of the asset-return-generating process as known with certainty. Both assumptions are extremely unrealistic. We will discuss the pernicious effects of ignoring either of these considerations, including some subtle ways in which they interact. We will then formulate a portfolio optimization problem which is aware both of market impact and model uncertainty and derive a solution for it. This is joint work with Lee Dicker. Speaker(s): Jerome Beneviste (NYU- Courant)