A computer-implemented system and method for executing trades of financial securities according to a combination passive/aggressive trading strategy that reliably executes trades of lists of securities or blocks of a single security within a desired time frame while taking advantage of dynamic market movement to realize price improvement for the trade within the desired time frame. A passive trading agent executes trades at advantageous prices by floating portions of the order at the bid or ask to maximize exposure to the inside market and attract market orders. An aggressive agent opportunistically takes liquidity as it arises, setting discretionary prices in accordance with historical trading data of the specified security.