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- Sophie Laruelle, Charles-Albert Lehalle, Gilles Pagès
- SIAM J. Financial Math.
- 2011

Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions… (More)

Market makers have to continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we provide… (More)

This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss in [2], or only on the liquidity-consuming orders like Obizhaeva and Wang in [31], we link the optimal trade-schedule to the price of the limit orders that have to be sent to the limit… (More)

- Bruno Bouchard, Ngoc-Minh Dang, Charles-Albert Lehalle
- SIAM J. Financial Math.
- 2011

We propose a general framework for intra-day trading based on the control of trading algorithms. Given a generic parameterized algorithm, we control the dates (τi)i at which it is launched, the length (δi)i of the trading period and the value of the parameters (Ei)i kept during the time interval [τi, τi + δi[. This gives rise to a non-classical impulse… (More)

- Emmanuel Bacry, Adrian Iuga, Matthieu Lasnier, Charles-Albert Lehalle
- 2014

In this paper, we use a database of around 400,000 metaorders issued by investors and electronically traded on European markets in 2010 in order to study market impact at different scales. At the intraday scale we confirm a square root temporary impact in the daily participation, and we shed light on a duration factor in 1/T γ with γ ' 0.25. Including this… (More)

Considering that a trader or a trading algorithm interacting with markets during continuous auctions can be modeled by an iterating procedure adjusting the price at which he posts orders at a given rhythm, this paper proposes a procedure minimizing his costs. We prove the a.s. convergence of the algorithm under assumptions on the cost function and give some… (More)

We derive explicit recursive formulas for Target Close (TC) and Implementation Shortfall (IS) in the Almgren-Chriss framework. We explain how to compute the optimal starting and stopping times for IS and TC, respectively, given a minimum trading size. We also show how to add a minimum participation rate constraint (Percentage of Volume, PVol) for both TC… (More)

This paper studies four trading algorithms of a professional trader, in a realistic two-sided limit order book whose dynamics are driven by the order book events. The identity of the trader can be either privileged or regular, either a hedge fund or a brokery agency. The speed and cost of trading can be balanced by properly choosing active strategies on the… (More)

Real-time market microstructure analysis: online transaction cost analysis R. Azencott, A. Beri, Y. Gadhyan, N. Joseph, C.-A. Lehalle & M. Rowley a Department of Mathematics, University of Houston, Houton, TX, USA b Ecole Normale Supérieure Cachan, Cachan, France c Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA d Cluster… (More)

Automatic differentiation has been involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic differentiation can be used. In between formal derivation and standard numerical schemes, this approach is based on… (More)