Article

# Optimal execution strategies in limit order books with general shape functions

Quantitative Finance (Impact Factor: 0.82). 08/2007; DOI: 10.2139/ssrn.1510104

Source: OAI

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**ABSTRACT:**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 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.Mathematical Finance 01/2014; · 1.25 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In limit order book markets, traders face the problem whether to display or hide their orders. While hiding reduces exposure impact, exposing can increase execution priority. Based on order flow dynamics, we develop a structural model that captures this trade-off. A central aspect of this work is the market impact of exposure: exposed limit orders affect incoming order flow. We derive explicit characterizations of the optimal exposure strategy under various market specifications. Using high-resolution ITCH data, we estimate the true impact of the exposure and calculate the optimal exposure for various stocks under high-frequency trading horizons. It turns out that exposure does mainly affect the supply side of liquidity. Our results suggests that the use of hidden orders can significantly increase trade performance.05/2014; -
##### Article: Trading with Small Price Impact

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**ABSTRACT:**An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth. In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general Markovian setting allowing for stochastic market, cost, and preference parameters. These results shed light on the general structure of the problem at hand, and also unveil close connections to optimal execution problems and to other market frictions such as proportional and fixed transaction costs.02/2014;

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