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We consider a framework for solving optimal liquidation problems in limitorder books. In particular, order arrivals are modeled as a point process whoseintensity depends on the liquidation price. We set up a stochastic controlproblem in which the goal is to maximize the expected revenue from liquidatingthe entire position held. We solve this optimal liquidation problem forpower-law and exponential-decay order book models and discuss severalextensions. We also consider the continuous selling (or fluid) limit when thetrading units are ever smaller and the intensity is ever larger. This limitprovides an analytical approximation to the value function and the optimalsolution. Using techniques from viscosity solutions we show that the discretestate problem and its optimal solution converge to the corresponding quantitiesin the continuous selling limit uniformly on compacts.

Liquidation in Limit Order Books with Controlled Intensity