Abstracts

We propose a model for limit order books with stochastic, reverse U-shaped, market depth, consistent with empirical studies. Stochastic market depth is necessary to accommodate various order activities, such as limit order submission at and outside the best quotes and order cancellation, which may account for a large proportion of limit order activities. To show the analytical tractability of the model, in addition to a dynamic programming formulation of the optimal execution problem, we provide easily computable and tight upper and lower bounds for the optimal execution cost, as well as their resulting trading strategies via quadratic programming and jump-linear-quadratic control.