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* Corresponding author 1 CAMS - Centre d-analyse et de mathématique sociale 2 Head of Quantitative Research

Abstract : The efficient frontier is a core concept in Modern Portfolio Theory. Based on this idea, we will construct optimal trading curves for different types of portfolios. These curves correspond to the algorithmic trading strategies that minimize the expected transaction costs, i.e. the joint effect of market impact and market risk. We will study five portfolio trading strategies. For the first three single-asset, general multi-asseet and balanced portfolios we will assume that the underlyings follow a Gaussian diffusion, whereas for the last two portfolios we will suppose that there exists a combination of assets such that the corresponding portfolio follows a mean-reverting dynamics. The optimal trading curves can be computed by solving an N-dimensional optimization problem, where N is the pre-determined number of trading times. We will solve the recursive algorithm using the -shooting method-, a numerical technique for differential equations. This method has the advantage that its corresponding equation is always one-dimensional regardless of the number of trading times N. This novel approach could be appealing for high-frequency traders and electronic brokers.

Keywords : quantitative finance optimal trading algorithmic trading systematic trading market microstructure

Author: Mauricio Labadie - Charles-Albert Lehalle -

Source: https://hal.archives-ouvertes.fr/


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