Optimal Trading Strategies in a Limit Order Market with Imperfect Liquidity

We study the optimal execution strategy of selling a security. In a continuous time diffusion framework, a risk-averse trader faces the choice of selling the security promptly or placing a limit order and hence delaying the transaction in order to sell at a more favorable price. We introduce a random delay parameter, which defers limit order execution and characterizes market liquidity. The distribution of expected time-to-fill of limit orders conforms to the empirically observed exponential distribution of trading times, and its variance decreases with liquidity. We obtain a closed-form solution and demonstrate that the presence of the lag factor linearizes the impact of other market parameters on the optimal limit price. Finally, two more stylized facts are rationalized in our model: the equilibrium bid-ask spread decreases with liquidity, but increases with agents risk aversion.