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: arXiv

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**ABSTRACT:**Introducing a financial transaction tax (FTT) has recently attracted tremendous global attention, with both proponents and opponents disputing its dampening effects on financial markets. In this paper we present a model to show under some circumstances that there exists a win-win situation via optimal trading when the tax burden can be dispersed. The way to absorb FTT in our model is to adjust the bid-ask spread. In our optimal trading model that considers FTT, the representative traders depend on the liquidity (market depth) they supply to weight their associated transaction cost by adjusting the spread ex post. We illustrate the analytical properties and computational solutions of our model when finding the optimal trading strategy under different market situations in order to offset FTT. We also conduct a simulation study to show the superior performance of our proposed optimal trading strategy in comparison to the alternative strategies that do not consider absorbing FTT. The results demonstrate that there is indeed a win-win situation, because financial institutions will not be worse off if such an optimal trading strategy is applied to offset FTT and reduce their transaction cost.Computational Economics 10/2014; · 0.46 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider a multi-player situation in an illiquid market in which one player tries to liquidate a large portfolio in a short time span, while some competitors know of the seller's intention and try to make a profit by trading in this market over a longer time horizon. We show that the liquidity characteristics, the number of competitors and their trading time horizons determine the optimal strategy for the competitors: they either provide liquidity to the seller, or they prey by simultaneous selling. Depending on the expected competitor behavior, it might be sensible for the seller to pre-announce a trading intention ("sunshine trading") or to keep it secret ("stealth trading"). 0 The authors are grateful for the insightful suggestions of an anonymous referee, which greatly improved the paper. They moreover thank the Quantitative Products Group of Deutsche Bank, in particular Marcus Overhaus, for useful comments. This paper expresses the private opinion of the authors and does not necessarily reflect the views of Deutsche Bank.03/2009; - [Show abstract] [Hide abstract]

**ABSTRACT:**We develop an option pricing model based on a tug-of-war game. This two-player zero-sum stochastic differential game is formulated in the context of a multi-dimensional financial market. The issuer and the holder try to manipulate asset price processes in order to minimize and maximize the expected discounted reward. We prove that the game has a value and that the value function is the unique viscosity solution to a terminal value problem for a parabolic partial differential equation involving the non-linear and completely degenerate infinity Laplace operator.Mathematical Finance 10/2014; · 1.25 Impact Factor

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