DE MARCH Hadrien

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Affiliations
  • 2017 - 2019
    Centre de mathématiques appliquées
  • 2017 - 2018
    Ecole Polytechnique
  • 2017 - 2018
    Communauté d'universités et établissements Université Paris-Saclay
  • 2017 - 2018
    Ecole doctorale de mathematiques hadamard (edmh)
  • 2019
  • 2018
  • Optimal trading using signals.

    Hadrien DE MARCH, Charles albert LEHALLE
    2019
    In this paper we propose a mathematical framework to address the uncertainty emergingwhen the designer of a trading algorithm uses a threshold on a signal as a control. We rely ona theorem by Benveniste and Priouret to deduce our Inventory Asymptotic Behaviour (IAB)Theorem giving the full distribution of the inventory at any point in time for a well formulatedtime continuous version of the trading algorithm.Since this is the first time a paper proposes to address the uncertainty linked to the use of athreshold on a signal for trading, we give some structural elements about the kind of signals thatare using in execution. Then we show how to control this uncertainty for a given cost function.There is no closed form solution to this control, hence we propose several approximation schemesand compare their performances.Moreover, we explain how to apply the IAB Theorem to any trading algorithm drivenby a trading speed. It is not needed to control the uncertainty due to the thresholding of asignal to exploit the IAB Theorem. it can be applied ex-post to any traditional trading algorithm.
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