Spread crossing in a limit order book: optimal strategies and asymptotic analysis

We study when a precommitted trader converts a limit order to a market order inalgorithmic executions of orders. We formulate the problem as an optimal stopping problem. We present structural properties of the optimal... [ view full abstract ]

We study when a precommitted trader converts a limit order to a market order in
algorithmic executions of orders. We formulate the problem as an optimal stopping problem. We present structural properties of the optimal strategy and show how it depends on market conditions. We derive and rigorously prove high order asymptotic expansions for the optimal exercise boundary near expiry. Numerical experiments illustrate the accuracy of the approximation.