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arXiv · 1905.04821

Optimal multi-asset trading with linear costs: a mean-field approach

Matt Emschwiller·Benjamin Petit·Jean-Philippe Bouchaud
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Abstract

Optimal multi-asset trading with Markovian predictors is well understood in the case of quadratic transaction costs, but remains intractable when these costs are $L_1$. We present a mean-field approach that reduces the multi-asset problem to a single-asset problem, with an effective predictor that includes a risk averse component. We obtain a simple approximate solution in the case of Ornstein-Uhlenbeck predictors and maximum position constraints. The optimal strategy is of the "bang-bang" type similar to that obtained in [de Lataillade et al., 2012]. When the risk aversion parameter is small, we find that the trading threshold is an affine function of the instantaneous global position, with a slope coefficient that we compute exactly. We relate the risk aversion parameter to the desired target risk and provide numerical simulations that support our analytical results.

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Matt Emschwiller, Benjamin Petit, Jean-Philippe Bouchaud. 2019-05-13. Optimal multi-asset trading with linear costs: a mean-field approach. https://arxiv.org/abs/1905.04821

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