Optimal split of orders across liquidity pools: A stochastic algorithm approach

SIAM Journal on Financial Mathematics

Volumn 2, Issue 1, 2011, Pages 1042-1076

  Laruelle, Sophie ^a   Lehalle, Charles Albert ^b   Pagés, Gilles ^a  

^a SORBONNE UNIVERSITÉ   (France)

^b CA CIB group   (France)

Author keywords

Asset allocation; Market impact; Monotone dynamic system; Reinforcement principle; Stochastic approximation; Stochastic Lagrangian algorithm

Indexed keywords

EID: 84860523383     PISSN: None     EISSN: 1945497X     Source Type: Journal    
DOI: 10.1137/090780596     Document Type: Article

References (34)

1. A. Alfonsi A. Fruth and A. Schied Optimal execution strategies in limit order books with general shape functions Quant. Finance 10 (2010) pp. 143-157.
2. A. Alfonsi A. Schied and A. Slynko Order Book Resilience Price Manipulation and the Positive Portfolio Problem Social Science Research Network Working Paper Series 2009.
3. R. Almgren and B. Harts A Dynamic Algorithm for Smart Order Routing Tech. report StreamBase 2008.
4. R. F. Almgren and N. Chriss Optimal execution of portfolio transactions J. Risk 3 (2000) pp. 5-39.
5. Y. Amihud and H. Mendelson Multimarket trading: A self-regulatory proposal in Global Equity Markets: Technological Competitive and Regulatory Challenges Irwin Professional Publishing Chicago 1995 pp. 340-349.
6. M. Avellaneda and S. Stoikov High-frequency trading in a limit order book Quant. Finance 8 (2008) pp. 217-224.
7. A. Benveniste M. M'etivier and P. Priouret Adaptive Algorithms and Stochastic Approximations Appl. Math. (N. Y.) 22 Springer-Verlag Berlin 1990.
8. R. Berenstein Algorithmes stochastiques microstructure et ex'ecution d'ordres Master 2 internship report (Quantitative Research Dir. C.-A. Lehalle CA Cheuvreux) Probabilit'es & Finance UPMC- ́ecole Polytechnique Paris 2008.
9. B. Bouchard N.-M. Dang and C.-A. Lehalle Optimal control of trading algorithms: A general impulse control approach SIAM J. Financial Math. 2 (2011) pp. 404-438.
10. K. J. Cohen S. F. Maier R. A. Schwartz and D. K. Whitcomb Market makers and the market spread: A review of recent literature J. Financ. Quant. Anal. 14 (1979) pp. 813-835.
11. J. Dedecker P. Doukhan G. Lang J. R. Le'on S. Louhichi and C. Prieur Weak Dependence: With Examples and Applications Lecture Notes in Statist. 190 Springer New York 2007.
12. P. Doukhan Mixing: Properties and Examples Lecture Notes in Statist. 85 Springer-Verlag New York 1994.
13. M. Duflo Random Iterative Models Appl. Math. (N. Y.) 34 Springer-Verlag Berlin 1997.
14. R. F. Engle R. Ferstenberg and J. R. Russell Measuring and Modeling Execution Cost and Risk Social Science Research Network Working Paper Series 2008.
15. T. Foucault and A. J. Menkveld Competition for order flow and smart order routing systems J. Finance 63 (2006) pp. 119-158.
16. K. Ganchev M. Kearns Y. Nemyvaka and J. Vaughan Censored exploration and the dark pool problem Comm. ACM 53 (2010) pp. 99-107.
17. F. R. Gantmacher The Theory of Matrices Vol. 1 AMS Chelsea Publishing Providence RI 1998. Reprint of the 1959 translation.
18. J. Gatheral No-dynamic-arbitrage and market impact Quant. Finance 10 (2010) pp. 749-759.
19. M. W. Hirsch and H. Smith Monotone Dynamical Systems monography 2004.
20. M. W. Hirsch and H. Smith Monotone dynamical systems in Handbook of Differential Equations: Ordinary Differential Equations. Vol. II Elsevier B. V. Amsterdam 2005 pp. 239-357.
21. H. J. Kushner and G. G. Yin Stochastic Approximation and Recursive Algorithms and Applications 2nd ed. Appl. Math. (N. Y.) 35 Springer-Verlag New York 2003.
22. A. P. Kyle Continuous auctions and insider trading Econometrica 53 (1985) pp. 1315-1335.
23. D. Lamberton and G. Pagés How fast is the bandit? Stoch. Anal. Appl. 26 (2008) pp. 603-623.
24. D. Lamberton and G. Pagés A penalized bandit algorithm Electron. J. Probab. 13 (2008) pp. 341- 373.
25. D. Lamberton G. Pagés and P. Tarrés When can the two-armed bandit algorithm be trusted? Ann. Appl. Probab. 14 (2004) pp. 1424-1454.
26. S. Laruelle Analyse d'algorithmes stochastiques appliqu'es á la Finance Thése de l'UPMC UPMC Paris 2011.
27. S. Laruelle and G. Pagés Stochastic approximation with averaging innovation Monte Carlo Methods Appl. to appear.
28. C.-A. Lehalle Rigorous strategic trading: Balanced portfolio and mean-reversion J. Trading 4 (2009) pp. 40-46.
29. C.-A. Lehalle O. Gu'eant and J. Razafinimanana High-frequency simulations of an order book: A two-scale approach in Econophysics of Order-Driven Markets F. Abergel B. K. Chakrabarti A. Chakraborti and M. Mitra eds. Springer Milan 2011 pp. 73-92.
30. V. Lemaire and G. Pagés Unconstrained recursive importance sampling Ann. Appl. Probab. 20 (2010) pp. 1029-1067.
31. A. J. Menkveld Splitting orders in overlapping markets: A study of cross-listed stocks J. Financ. Intermediation 17 (2008) pp. 145-174.
32. S. Predoiu G. Shaikhet and S. Shreve Optimal execution in a general one-sided limit-order book SIAM J. Financial Math. 2 (2011) pp. 183-212.
33. P. Tarrés Traps of Stochastic Algorithms and Vertex-Reinforced Random Walks Ph.D. thesis ENS Cachan Cachan France 2001.
34. N. G. Torre and M. J. Ferrari The Market Impact Model Handbook Tech. report BARRA Research Insights 1999.