High Frequency Trading In A Markov Renewal Model
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High Frequency Trading in a Markov Renewal Model
Author | : Pietro Fodra |
Publisher | : |
Total Pages | : 26 |
Release | : 2013 |
Genre | : |
ISBN | : |
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We study an optimal high frequency trading problem within a market micro-structure 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 bi-dimensional Euler scheme. Statistical procedures and numerical tests for computing the optimal limit order strategies illustrate our results.
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