O. [. Achdou and . Pironneau, Computational methods for option pricing, Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), vol.30, 2005.
DOI : 10.1137/1.9780898717495
URL : https://hal.archives-ouvertes.fr/hal-00111740

A. [. Alfonsi, A. Fruth, and . Schied, Constrained portfolio liquidation in a limit order book model, Advances in Mathematics of Finance, pp.9-25, 2008.
DOI : 10.4064/bc83-0-1

A. [. Alfonsi, A. Fruth, and . Schied, Optimal execution strategies in limit order books with general shape functions, Quantitative Finance, vol.10, issue.2, pp.143-157, 2010.
DOI : 10.1080/14697680500244411
URL : https://hal.archives-ouvertes.fr/hal-00166969

A. Alfonsi and A. Schied, Optimal Trade Execution and Absence of Price Manipulations in Limit Order Book Models, ASS11] A. Alfonsi, A. Schied, and A. Slynko. Order book resilience, price manipulation and the positive portfolio problem. SSRN eLibrary, pp.490-522, 2010.
DOI : 10.1137/090762786
URL : https://hal.archives-ouvertes.fr/hal-00397652

A. F. Almgren, Optimal execution with nonlinear impact functions and trading-enhanced risk, Applied Mathematical Finance, vol.3, issue.1, pp.1-18, 2003.
DOI : 10.3905/jpm.1992.409428

N. [. Almgren and . Chriss, Optimal execution of portfolio transactions, The Journal of Risk, vol.3, issue.2, pp.5-39, 2000.
DOI : 10.21314/JOR.2001.041

E. [. Almgren, H. Hauptmann, C. Li, and . Thum, Direct estimation of equity market impact, Risk, vol.18, pp.57-62, 2005.

J. [. Almgren and . Lorenz, Adaptive arrival price Algorithmic Trading III: Precision, Control, Execution, 2007.

F. [. Ammar, R. Chinesta, B. Keunings, and . Mokdad, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, Journal of Non-Newtonian Fluid Mechanics, vol.139, issue.3, pp.153-176, 2006.
DOI : 10.1016/j.jnnfm.2006.07.007
URL : https://hal.archives-ouvertes.fr/hal-01004909

M. Avellaneda, G. Davis, and S. Mallat, Adaptive greedy approximations, Constr. Approx, vol.13, issue.1, pp.57-98, 1997.

M. Avellaneda and S. Stoikov, High-frequency trading in a limit order book, Quantitative Finance, vol.8, issue.3, pp.217-224, 2008.
DOI : 10.1080/14697680500244411

T. [. Bader and . Kolda, Tensor decompositions and applications, SIAM Rev, vol.51, issue.3, pp.455-500, 2009.

A. [. Bank and . Fruth, Optimal Order Scheduling for Deterministic Liquidity Patterns, SIAM Journal on Financial Mathematics, vol.5, issue.1, 2012.
DOI : 10.1137/120897511
URL : http://arxiv.org/abs/1310.3077

. A. Bcdd08, A. Barron, W. Cohen, R. Dahmen, and . Devore, Approximation and learning by greedy algorithms, Annals of Statistics, vol.36, issue.1, pp.64-94, 2008.

A. [. Bertsimas and . Lo, Optimal control of execution costs, Journal of Financial Markets, vol.1, issue.1, pp.1-50, 1998.
DOI : 10.1016/S1386-4181(97)00012-8

B. Biais, P. Hillion, and C. Spatt, An empirical analysis of the limit order book and the order flow in the Paris Bourse The pricing of options and corporate liabilities, The Journal of Finance Journal of Political Economy, vol.50, issue.53, pp.1655-1689, 1973.

+. Bddl, C. Bouchaud, J. Deremble, J. De-lataillade, Y. Kockelkoren et al., Anomalous price impact and the critical nature of liquidity in financial markets, Phys. Rev. X, vol.1, p.21006, 2011.

J. Bouchaud, Y. Gefen, M. Potters, and M. Wyart, Fluctuations and response in financial markets: the subtle nature of ???random??? price changes, Quantitative Finance, vol.62, issue.2, pp.176-190, 2004.
DOI : 10.1080/713665670

[. Bouchaud and M. Potters, More statistical properties of order books and price impact. Physica A: Statistical Mechanics and its Applications, Proceedings of the International Econophysics Conference, pp.133-140, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00134675

[. Bris, T. Lelièvre, and Y. Maday, Results and Questions on a Nonlinear Approximation Approach for Solving High-dimensional Partial Differential Equations, Constructive Approximation, vol.17, issue.2, pp.621-651, 2009.
DOI : 10.1007/s00365-009-9071-1
URL : https://hal.archives-ouvertes.fr/inria-00336911

L. [. Brunnermeier and . Pedersen, Predatory Trading, The Journal of Finance, vol.75, issue.4, pp.1825-1863, 2005.
DOI : 10.1111/j.1540-6261.2005.00781.x

M. [. Bungartz and . Griebel, Sparse grids, Acta Numerica, vol.13, pp.147-269, 2004.
DOI : 10.1017/S0962492904000182

V. [. Cancès, T. Ehrlacher, and . Lelièvre, Convergence of a greedy algorithm for highdimensional convex nonlinear problems, Mathematical Models and Methods in Applied Sciences, 2012.

M. [. Carlin, S. Lobo, and . Viswanathan, Episodic Liquidity Crises: Cooperative and Predatory Trading, The Journal of Finance, vol.11, issue.5, pp.2235-2274, 2007.
DOI : 10.1111/j.1540-6261.2007.01274.x

D. [. Carr, R. H. Madan, and . Smith, Option valuation using the fast Fourier transform, The Journal of Computational Finance, vol.2, issue.4, pp.61-73, 1999.
DOI : 10.21314/JCF.1999.043

R. [. Çetin, P. Jarrow, and . Protter, Liquidity risk and arbitrage pricing theory

R. [. Chordia, A. Roll, and . Subrahmanyam, Market Liquidity and Trading Activity, The Journal of Finance, vol.33, issue.2, pp.501-530, 2001.
DOI : 10.1111/0022-1082.00335

A. [. Cont and . De-larrard, Price dynamics in a Markovian limit order market, Social Science Research Network Working Paper Series, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00832155

]. V. De-silva and L. Lim, Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem, SIAM Journal on Matrix Analysis and Applications, vol.30, issue.3, pp.1084-1127, 2008.
DOI : 10.1137/06066518X

R. [. Devore, C. Howard, and . Micchelli, Optimal nonlinear approximation, Manuscripta Mathematica, vol.29, issue.4, pp.469-478, 1989.
DOI : 10.1007/BF01171759

V. [. Devore and . Temlyakov, Some remarks on greedy algorithms, Advances in Computational Mathematics, vol.102, issue.1, pp.173-187, 1996.
DOI : 10.1007/BF02124742

[. Duffie, D. Filipovi?, and W. Schachermayer, Affine processes and applications in finance, Annals of Applied Probability, vol.13, pp.984-1053, 2003.
DOI : 10.3386/t0281

D. Duffie, J. Pan, and K. Singleton, Transform Analysis and Asset Pricing for Affine Jump-diffusions, Econometrica, vol.68, issue.6, pp.1343-1376, 2000.
DOI : 10.1111/1468-0262.00164

B. [. Eldén and . Savas, A Newton???Grassmann Method for Computing the Best Multilinear Rank-$(r_1,$ $r_2,$ $r_3)$ Approximation of a Tensor, SIAM Journal on Matrix Analysis and Applications, vol.31, issue.2, pp.248-271, 2009.
DOI : 10.1137/070688316

J. Fernandez, O. Guéant, and C. Lehalle, Optimal portfolio liquidation with limit orders, SIAM Journal on Financial Mathematics, vol.3, issue.1, pp.740-764, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00628533

E. [. Figueroa and . Suli, Greedy Approximation of High-Dimensional Ornstein???Uhlenbeck Operators, Foundations of Computational Mathematics, vol.11, issue.3, pp.573-623, 2012.
DOI : 10.1007/s10208-012-9122-z

T. [. Fruth, M. Schöneborn, and . Urusov, OPTIMAL TRADE EXECUTION AND PRICE MANIPULATION IN ORDER BOOKS WITH TIME-VARYING LIQUIDITY, Mathematical Finance, vol.2, issue.4, 2013.
DOI : 10.1111/mafi.12022

R. Gatheral, No-dynamic-arbitrage and market impact, Quantitative Finance, vol.8, issue.7, pp.749-759, 2010.
DOI : 10.1080/14697680500244411
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.377.7210

J. Gatheral, A. Schied, and A. Slynko, TRANSIENT LINEAR PRICE IMPACT AND FREDHOLM INTEGRAL EQUATIONS, Mathematical Finance, vol.2, issue.1, pp.445-474, 2012.
DOI : 10.1111/j.1467-9965.2011.00478.x

M. S. Gerety and J. H. Mulherin, Trading Halts and Market Activity: An Analysis of Volume at the Open and the Close, The Journal of Finance, vol.40, issue.5, pp.1765-1784, 1992.
DOI : 10.1111/j.1540-6261.1992.tb04682.x

J. [. Hamao, W. Hasbrouck-huberman, and . Stanzl, Securities Trading in the Absence of Dealers: Trades and Quotes on the Tokyo Stock Exchange, Review of Financial Studies, vol.8, issue.3, pp.849-8781247, 1995.
DOI : 10.1093/rfs/8.3.849

G. [. Jain and . Joh, The Dependence between Hourly Prices and Trading Volume, The Journal of Financial and Quantitative Analysis, vol.23, issue.3
DOI : 10.2307/2331067

D. [. Kempf and . Mayston, LIQUIDITY COMMONALITY BEYOND BEST PRICES, Journal of Financial Research, vol.24, issue.1, pp.25-40, 2008.
DOI : 10.2307/2327796

I. [. Kleidon and U. U. Werner, trading of British cross-listed stocks: an intraday analysis of market integration, KSS11] F. Klöck, A. Schied, and Y. Sun. Price manipulation in a market impact model with dark pool. Social Science Research Network Working Paper Series, pp.619-664, 1996.

V. [. Konyagin and . Temlyakov, Rate of convergence of pure greedy algorithm, East Journal on Approximations, vol.5, pp.493-499, 1999.

S. [. Kudryavtsev and . Levendorskii, Fast and accurate pricing of barrier options under L??vy processes, Finance and Stochastics, vol.10, issue.4, pp.531-562, 2009.
DOI : 10.1007/s00780-009-0103-2

]. P. Lad99 and . Ladevèze, Nonlinear computational structural mechanics: new approaches and nonincremental methods of calculations, 1999.

]. L. Lmv00a, B. De-lathauwer, . De, J. Moor, and . Vandewalle, A multilinear singular value decomposition, SIAM Journal on Matrix Analysis and Applications, vol.21, pp.1253-1278, 2000.

L. De-lathauwer, B. De, J. Moor, and . Vandewalle, ) Approximation of Higher-Order Tensors, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.4, pp.1324-1342, 2000.
DOI : 10.1137/S0895479898346995

C. [. Leentvaar and . Oosterlee, Multi-asset option pricing using a parallel Fourier-based technique, The Journal of Computational Finance, vol.12, issue.1, pp.1-26, 2008.
DOI : 10.21314/JCF.2008.184

J. Lorenz, J. C. Osterriedermer76-]-r, and . Merton, Simulation of a limit order driven market. The Journal Of Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, vol.3, issue.12, pp.125-144, 1976.

]. A. Nou10 and . Nouy, Proper generalized decompositions for a priori model reduction of problems formulated in tensor product spaces: Alternative definitions and algorithms, Proceedings of the Seventh International Conference on Engineering Computational Technology, 2010.

J. [. Obizhaeva and . Wang, Optimal trading strategy and supply/demand dynamics, 2005.
DOI : 10.1016/j.finmar.2012.09.001
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.181.198

[. Petersdorff and C. Schwab, Numerical solution of parabolic equations in high dimensions, ESAIM: Mathematical Modelling and Numerical Analysis, vol.38, issue.1, pp.93-127, 2004.
DOI : 10.1051/m2an:2004005

]. D. Pom08 and . Pommier, Méthodes numériques sur des grilles sparse appliquées à l'évaluation d'options en finance, 2008.

G. [. Predoiu, S. Shaikhet, and . Shreve, Optimal Execution in a General One-Sided Limit-Order Book, SIAM Journal on Financial Mathematics, vol.2, issue.1, pp.183-212, 2011.
DOI : 10.1137/10078534X

P. [. Rosenow and . Weber, Order book approach to price impact, Quantitative Finance, vol.5, issue.4, pp.357-364, 2005.

T. [. Schied and . Schöneborn, Risk aversion and the dynamics of optimal liquidation strategies in??illiquid markets, Finance and Stochastics, vol.5, issue.2, pp.181-204, 2009.
DOI : 10.1007/s00780-008-0082-8

]. S. Smo63 and . Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Soviet Mathematics Doklady, vol.3, pp.240-243, 1963.

]. V. Tem08 and . Temlyakov, Greedy approximation, Acta Numerica, vol.17, pp.235-409, 2008.

]. C. Zen91 and . Zenger, Sparse grids, Parallel algorithms for partial differential equations, pp.241-251, 1990.