, des quantités despremì eres limites, et des positions des ordres placés placésà l'achat etàetà la vente. Mais ce serait un grand succès si leprobì eme sera résolu

J. 'estime, espère que cette thèse apporte des nouveautésnouveautésà la fois aux chercheurs académiques et industriels. La communauté académique bénéficie des observations empiriquement importantes, et quelques solutionsàsolutionsà l'aide des outils mathématiques avancés sont proposées. Elle a aussi aidé monéquipemonéquipe d'accueil, Automated Market Making du BNP Paribas

, Enfin, je remercie sincèrementsincèrementà tous ceux qui m'ont aidéaidéà réaliser ce travail, p.98

. Mifid, Article 17.4, Limit order books, 2016.

, Algorithmic trading in a microstructural limit order book model, 2017.

F. Abergel and A. Jedidi, Long-time behavior of a Hawkes process-based limit order book, SIAM Journal on Financial Mathematics, vol.6, pp.1026-1043, 2015.
DOI : 10.1137/15m1011469
URL : https://hal.archives-ouvertes.fr/hal-01121711

A. , An empirical comparison of machine learning models for time series forecasting, Econometric Reviews, vol.29, issue.5-6, pp.594-621, 2010.

M. Anane and . Andersen, Une approche mathématique de l'investissement boursier, Great realizations. Risk, vol.13, pp.105-108, 2000.

W. Antweiler and M. Z. Frank, Is all that talk just noise? the information content of internet stock message boards, The Journal of finance, vol.59, issue.3, pp.761-782, 2004.

S. Avellaneda, M. Avellaneda, and S. Stoikov, High frequency trading in a limit order book, Quantitative Finance, vol.8, issue.3, pp.217-224, 2008.

[. Bacry, Modelling microstructure noise with mutually exciting point processes, Quantitative Finance, vol.13, issue.1, pp.65-77, 2013.
DOI : 10.1080/14697688.2011.647054
URL : https://hal.archives-ouvertes.fr/hal-00830987

[. Bacry, Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics, Quantitative Finance, vol.16, issue.8, pp.1179-1201, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01313833

[. Bacry, Hawkes processes in finance, Market Microstructure and Liquidity, issue.01, p.1, 2015.
DOI : 10.1142/s2382626615500057
URL : https://hal.archives-ouvertes.fr/hal-01313838

E. Bacry and J. Muzy, Hawkes model for price and trades high-frequency dynamics, Quantitative Finance, vol.14, issue.7, pp.1147-1166, 2014.
DOI : 10.1080/14697688.2014.897000
URL : https://hal.archives-ouvertes.fr/hal-01313840

N. Rieder-;-bäuerle and U. Rieder, Markov decision processes with applications to finance, 2011.

L. Bayraktar, E. Bayraktar, and M. Ludkovski, Liquidation in limit order books with controlled intensity, Mathematical Finance, vol.24, issue.4, pp.627-650, 2014.

[. Bouchaud, How markets slowly digest changes in supply and demand, Handbook of Financial Markets: Dynamics and Evolution, pp.57-156, 2009.

C. G. Bowsher, Modelling security market events in continuous time: Intensity based, multivariate point process models, Journal of Econometrics, vol.141, issue.2, pp.876-912, 2007.

M. Brémaud, P. Brémaud, and L. Massoulié, Stability of nonlinear Hawkes processes, Ann. Probab, vol.24, pp.1563-1588, 1996.

[. Brogaard, High-frequency trading and price discovery, The Review of Financial Studies, vol.27, issue.8, pp.2267-2306, 2014.

[. Cartea, Enhancing trading strategies with order book signals, Applied Mathematical Finance, pp.1-35, 2018.
DOI : 10.1080/1350486x.2018.1434009

´. A. Cartea, S. Jaimungal, ´. A. Cartea, S. Jaimungal, and . Cartea, Risk metrics and fine tuning of high frequency trading strategies, SIAM Journal of Financial Mathematics, vol.20, issue.1, pp.415-444, 2013.

[. Chakraborti, Econophysics review: I. empirical facts, Quantitative Finance, vol.11, issue.7, pp.991-1012, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00621058

D. Cont, R. Larrard-;-cont, and A. De-larrard, Price dynamics in a Markovian limit order book market, SIAM Journal on Financial Mathematics, vol.4, pp.1-25, 2013.

[. Cont, The price impact of order book events, Journal of financial econometrics, vol.12, issue.1, pp.47-88, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00545745

[. Cont, A stochastic model for order book dynamics, Operations Research, vol.58, pp.549-563, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00497666

. Das, Recent advances in differential evolution-an updated survey, Swarm and Evolutionary Computation, vol.27, pp.1-30, 2016.

[. Dean, Large scale distributed deep networks, Advances in neural information processing systems, pp.1223-1231, 2012.

[. Eisler, The price impact of order book events: market orders, limit orders and cancellations, Quantitative Finance, vol.12, issue.9, pp.1395-1419, 2012.

T. Fischer and C. Krauss, Deep learning with long short-term memory networks for financial market predictions, European Journal of Operational Research, 2017.

P. Pham-;-fodra, H. Pham, P. Fodra, and H. Pham, High frequency trading and asymptotics for small risk aversion in a markov renewal model, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01261362

Y. Gal and Z. Ghahramani, , 2016.

[. Gers, Statistical properties of share volume traded in financial markets, Physical Review E, vol.62, issue.4, p.4493, 1999.

B. Gould, M. D. Gould, and J. Bonart, Queue imbalance as a one-tick-ahead price predictor in a limit order book, Market Microstructure and Liquidity, vol.2, issue.02, p.1650006, 2016.

[. Gu, General intensity shapes in optimal liquidation, Mathematical Finance, vol.25, issue.3, pp.457-495, 2015.

P. Guilbaud, F. Guilbaud, and H. Pham, Optimal high frequency trading in a pro-rata microstructure with predictive information, Mathematical Finance, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00697125

. Pham, F. Guilbaud, and H. Pham, Optimal high-frequency trading with limit and market orders, Quantitative Finance, vol.13, pp.79-94, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00603385

[. Guéant, Optimal portfolio liquidation with limit orders, SIAM Journal on Financial Mathematics, vol.3, issue.1, pp.740-764, 2012.

[. Guéant, Dealing with the inventory risk: a solution to the market making problem, Mathematics and financial economics, vol.7, pp.477-507, 2013.

O. Hawkes, A. G. Hawkes, and D. Oakes, A cluster process representation of a Self-Exciting process, Journal of Applied Probability, vol.11, pp.493-503, 1974.

[. Heaton, Deep learning in finance, 2016.

. Ho, T. Ho, and H. R. Stoll, Optimal dealer pricing under transactions and return uncertainty, The Journal of Trading, vol.9, pp.47-73, 1981.

S. Hochreiter and J. Schmidhuber, Long short-term memory, Neural computation, vol.9, issue.8, pp.1735-1780, 1997.

[. Hornik, Multilayer feedforward networks are universal approximators, Neural networks, vol.2, issue.5, pp.359-366, 1989.
DOI : 10.1016/0893-6080(89)90020-8

. Huang, Simulating and analyzing order book data: The queue-reactive model, Journal of the American Statistical Association, vol.110, pp.107-122, 2015.
DOI : 10.1080/01621459.2014.982278
URL : https://hal.archives-ouvertes.fr/hal-01172326

. Huang, Simulating and analyzing order book data: The queue-reactive model, Journal of the American Statistical Association, vol.110, issue.509, pp.107-122, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01172326

W. Huang and M. Rosenbaum, Ergodicity and diffusivity of markovian order book models: a general framework, SIAM Journal on Financial Mathematics, vol.8, issue.1, pp.874-900, 2017.

H. Hult and J. Kiessling, Algorithmic trading with Markov chains, 2010.

T. Jaisson, Market impact as anticipation of the order flow imbalance, Quantitative Finance, vol.15, issue.7, pp.1123-1135, 2015.

K. Kim-;-kim, Financial time series forecasting using support vector machines, Neurocomputing, vol.55, issue.1-2, pp.307-319, 2003.

C. Krauss, Statistical arbitrage pairs trading strategies: Review and outlook, Journal of Economic Surveys, vol.31, issue.2, pp.513-545, 2017.
DOI : 10.1111/joes.12153
URL : https://www.econstor.eu/bitstream/10419/116783/1/833997289.pdf

J. Large, Measuring the resiliency of an electronic limit order book, Journal of Financial Markets, vol.10, pp.1-25, 2007.
DOI : 10.1016/j.finmar.2006.09.001
URL : http://users.iems.northwestern.edu/~armbruster/2007msande444/large-06.pdf

C. Lehalle and O. Mounjid, Limit order strategic placement with adverse selection risk and the role of latency, Market Microstructure and Liquidity, vol.3, issue.01, p.1750009, 2017.

Y. Zhang-;-li and J. Zhang, A differential evolution algorithm with dynamic population partition and local restart, Proceedings of the 13th annual conference on Genetic and evolutionary computation, pp.1085-1092, 2011.

X. Lu and F. Abergel, High-dimensional hawkes processes for limit order books: modelling, empirical analysis and numerical calibration, Quantitative Finance, vol.18, issue.2, pp.249-264, 2018.
DOI : 10.1080/14697688.2017.1403142
URL : https://hal.archives-ouvertes.fr/hal-01686122

[. Lu, X. Lu, and F. Abergel, Order-book modelling and market making strategies, 2018.
DOI : 10.1142/s2382626619500035
URL : http://arxiv.org/pdf/1806.05101

L. Massoulié-;-massoulié, Stability results for a general class of interacting point processes dynamics, and applications, Stochastic Processes and their Applications, vol.75, pp.1-30, 1998.

[. Moro, Market impact and trading profile of large trading orders in stock markets, 2009.

[. Muni-toke-;-muni-toke and I. , The order book as a queueing system: average depth and influence of the size of limit orders, Quantitative Finance, vol.15, issue.5, pp.795-808, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01006410

[. Muni-toke-;-muni-toke and I. , Reconstruction of order flows using aggregated data. Market microstructure and liquidity, 2017.

. Nelson, Stock market's price movement prediction with lstm neural networks, 2017 International Joint Conference on, pp.1419-1426, 2017.
DOI : 10.1109/ijcnn.2017.7966019

O. Connor, From tweets to polls: Linking text sentiment to public opinion time series, Icwsm, vol.11, pp.1-2, 2010.

T. Ozaki, Maximum likelihood estimation of Hawkes' self-exciting point processes, Annals of the Institute of Statistical Mathematics, vol.31, pp.145-155, 1979.

. Patel, Predicting stock market index using fusion of machine learning techniques, Expert Systems with Applications, vol.42, issue.4, pp.2162-2172, 2015.

[. Radivojevi´cradivojevi´c, Ergodic transition in a simple model of the continuous double auction, PloS one, vol.9, issue.2, p.88095, 2014.

[. Rambaldi, The role of volume in order book dynamics: a multivariate hawkes process analysis, Quantitative Finance, vol.17, issue.7, pp.999-1020, 2017.

I. Rubin-;-rubin, Regular point processes and their detection, IEEE Transactions on Information Theory, 1972.

. Scalas, Waiting times between orders and trades in double-auction markets, Physica A: Statistical Mechanics and its Applications, vol.366, pp.463-471, 2006.

. Scalas, Low-traffic limit and first-passage times for a simple model of the continuous double auction, Physica A: Statistical Mechanics and its Applications, vol.485, pp.61-72, 2017.

[. Selvin, Stock price prediction using lstm, rnn and cnn-sliding window model, Advances in Computing, Communications and Informatics (ICACCI, pp.1643-1647, 2017.

[. Smith, Statistical theory of the continuous double auction, Quantitative Finance, vol.6, pp.481-514, 2003.

S. Stoikov, The micro-price, 2017.

P. ;. Storn, R. Storn, and K. Price, Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces, vol.3, 1995.

J. Stübinger and J. Bredthauer, Statistical arbitrage pairs trading with high-frequency data, International Journal of Economics and Financial Issues, vol.7, issue.4, 2017.

J. Stübinger and S. Endres, Pairs trading with a mean-reverting jump-diffusion model on high-frequency data, Quantitative Finance, pp.1-17, 2018.

M. Talih and N. Hengartner, Structural learning with time-varying components: tracking the cross-section of financial time series, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.67, issue.3, pp.321-341, 2005.

P. C. Tetlock, Giving content to investor sentiment: The role of media in the stock market, The Journal of finance, vol.62, issue.3, pp.1139-1168, 2007.

. Tetlock, More than words: Quantifying language to measure firms' fundamentals, The Journal of Finance, vol.63, issue.3, pp.1437-1467, 2008.

. Tieleman, T. Hinton-;-tieleman, and G. Hinton, Lecture 6.5-RmsProp: Divide the gradient by a running average of its recent magnitude, COURSERA: Neural Networks for Machine Learning, 2012.

[. Toth, How does the market react to your order flow?, Quantitative Finance, vol.12, issue.7, pp.1015-1024, 2012.

[. Wyart, Relation between bid-ask spread, impact and volatility in order-driven markets, Quantitative Finance, vol.8, issue.1, pp.41-57, 2008.

Y. , An improved adaptive differential evolution algorithm with population adaptation, Proceedings of the 15th annual conference on Genetic and evolutionary computation, pp.145-152, 2013.

T. Yang and L. Zhu, A reduced-form model for level-1 limit order books, Market Microstructure and Liquidity, vol.2, issue.02, p.1650008, 2016.

[. Zheng, Modelling bid and ask prices using constrained Hawkes processes: Ergodicity and scaling limit, SIAM Journal on Financial Mathematics, vol.5, pp.99-136, 2014.

[. Zheng, Asynchronous stochastic gradient descent with delay compensation for distributed deep learning, 2016.

L. Zhu, Large deviations for Markovian nonlinear Hawkes processes, The Annals of Applied Probability, vol.25, issue.2, pp.548-581, 2015.

, Algorithm 1 Differential Evolution algorithm 1: Input. Maximum total generation G, population size N ? 4, mutation factor F ? (0, 2), crossover rate CR ? (0, 1), parameter domain ?, termination criteria. 2: Output. optimal point (optimal function value, termination generation etc

.. .. , 1 ) randomly such that x i,1 ? ?; 5: while g ? G and termination criteria not met do 6: for i ? 1, Choose randomly r 1, vol.8

, Construct donner v i,g+1 ? x r 1 ,g + F (x r 2, vol.9

/. Crossover, Construct trial element u i,g+1 11: I rand is a random integer from 1, vol.12