Modeling uncertainty in limit order execution

• We study optimal trading strategies with limit orders.
• A stochastic dynamic programming problem is solved explicitly.
• Numerical examples illustrate traders’ behavior.
• A fuzzy version of the model is proposed too.

A model for limit order execution is developed where several sources of uncertainty are taken into account. We focus on the optimal trading strategy of an investor who has to buy a block of shares throughout the submission of limit orders. This trading problem is explicitly solved and we analyze how the state of the limit order book and the investor's subjective beliefs affect the optimal strategy.