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LIQUIDATION IN LIMIT ORDER BOOKS WITH CONTROLLED INTENSITY
Author(s) -
Bayraktar Erhan,
Ludkovski Michael
Publication year - 2014
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2012.00529.x
Subject(s) - limit (mathematics) , position (finance) , mathematical optimization , bellman equation , viscosity solution , order (exchange) , limit point , intensity (physics) , exponential function , stochastic control , optimal control , mathematics , mathematical economics , economics , finance , physics , mathematical analysis , quantum mechanics
We consider a framework for solving optimal liquidation problems in limit order books. In particular, order arrivals are modeled as a point process whose intensity depends on the liquidation price. We set up a stochastic control problem in which the goal is to maximize the expected revenue from liquidating the entire position held. We solve this optimal liquidation problem for power‐law and exponential‐decay order book models explicitly and discuss several extensions. We also consider the continuous selling (or fluid) limit when the trading units are ever smaller and the intensity is ever larger. This limit provides an analytical approximation to the value function and the optimal solution. Using techniques from viscosity solutions we show that the discrete state problem and its optimal solution converge to the corresponding quantities in the continuous selling limit uniformly on compacts.