High frequency trading in a Markov renewal model

Abstract : We study an optimal high frequency trading problem within a market microstructure model aiming at a good compromise between accuracy and tractability. The stock price is modeled by a Markov Renewal Process (MRP), while market orders arrive in the limit order book via a point process correlated with the stock price, and taking into account the adverse selection risk. We apply stochastic control methods in this semi-Markov framework, and show how to reduce remarkably the complexity of the associated Hamilton-Jacobi-Bellman equation by suitable change of variables that exploits the specific symmetry of the problem. We then handle numerically the remaining part of the HJB equation, simplified into an integro-ordinary differential equation, by a bidimensional Euler scheme. Statistical procedures and numerical tests for computing the optimal limit order strategies illustrate our results.
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Soumis le : vendredi 27 septembre 2013 - 16:20:04
Dernière modification le : jeudi 27 avril 2017 - 09:46:23
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  • HAL Id : hal-00867113, version 1

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UPMC | INSMI | USPC | PMA

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Pietro Fodra, Huyen Pham. High frequency trading in a Markov renewal model. 2013. 〈hal-00867113〉

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