Portfolio liquidation in dark pools in continuous time

Mathematical Finance

Volumn 25, Issue 3, 2015, Pages 496-544

  Kratz, Peter ^a   Schöneborn, Torsten ^b  

^a AIX MARSEILLE UNIVERSITY   (France)

^b DEUTSCHE BANK AG   (Germany)

Author keywords

Dark pools; Illiquid markets; Market microstructure; Optimal liquidation; Singular boundary condition; Stochastic control

Indexed keywords

EID: 84930382360     PISSN: 09601627     EISSN: 14679965     Source Type: Journal    
DOI: 10.1111/mafi.12037     Document Type: Article

References (51)

1. Alfonsi, A., A. Fruth, and A. Schied (2010): Optimal Execution Strategies in Limit Order Books with General Shape Functions. Quant. Finance 10(2), 143-157.
2. Almgren, R. (2003): Optimal Execution with Nonlinear Impact Functions and Trading-Enhanced Risk. Appl. Math. Finance 10(1), 1-18.
3. Almgren, R., and N. Chriss (2001): Optimal Execution of Portfolio Transactions. J. Risk 3(2), 5-39.
4. Almgren, R., and J. Lorenz (2007): Adaptive Arrival Price, in Algorithmic Trading III: Precision, Control, Execution, B. Bruce, ed. New York: Institutional Investor Inc., pp. 59-66.
5. Almgren, R., C. Thum, E. Hauptmann, and H. Li (2005): Direct Estimation of Equity Market Impact. Risk 18(7), 57-62.
6. Applebaum, D. (2004): Lévy Processes and Stochastic Calculus. Cambridge: Cambridge University Press.
7. Bayraktar, E., and M. Ludkovski (2014): Liquidation in Limit Order Books with Controlled Intensity. Math. Finance 24(4), 627-650.
8. Bernstein, D. S. (2005): Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory. Princeton: Princeton University Press.
9. Bertsimas, D., and A. Lo (1998): Optimal Control of Execution Costs. J. Finan. Markets 1(1), 1-50.
10. Bouchard, B., and N.-M. Dang (2013): Generalized Stochastic Target Problems for Pricing and Partial Hedging under Loss Constraints-Application in Optimal Book Liquidation. Finance Stoch. 17(1), 31-72.
11. Bouchard, B., R. Elie, and N. Touzi (2009): Stochastic Target Problems with Controlled Loss. SIAM J. Control Optim. 48(5), 3123-3150.
12. Carlin, B. I., M. Sousa Lobo, and S. Viswanathan (2007): Episodic Liquidity Crises: Cooperative and Predatory Trading. J. Finance 65(5), 2235-2274.
13. Carrie, C. (2008): Illuminating the New Dark Influence on Trading and U.S. Market Structure. J. Trading 3(2), 40-55.
14. Conrad, J., K. M. Johnson, and S. Wahal (2003): Institutional Trading and Alternative Trading Systems. J. Finan. Econ. 70(1), 99-134.
15. Coppel, W. A. (1971): Disconjugacy. Lecture Notes in Mathematics, Vol. 220. Berlin: Springer.
16. Degryse, H., M. Van Achter, and G. Wuyts (2009a): Dynamic Order Submission Strategies with Competition between a Dealer Market and a Crossing Network. J. Finan. Econ. 91(3), 319-338.
17. Degryse, H., M. Van Achter, and G. Wuyts (2009b): Shedding Light on Dark Liquidity Pools. Institutional Investor 2009(1), 147-155.
18. Dönges, J., and F. Heinemann (2013): Crossing Network versus Dealer Market: Unique Equilibria in the Allocation of Order Flow. Eur. Econ. Rev. 62, 41-57.
19. Fong, K., A. Madhavan, and P. L. Swan (2004): Upstairs, Downstairs: Does the Upstairs Market Hurt the Downstairs? Preprint. Available at: available online at: http://www.finance.nsysu.edu.tw/SFM/15thSFM/14thSFM/13thSFM/12thSFM/167970922.pdf. Accessed April 26, 2013.
20. Ganchev, K., M. Kearns, Y. Nevmyvaka, and J. Wortman Vaughan (2010): Censored Exploration and the Dark Pool Problem. Commun. ACM 53(5), 99-107.
21. Glosten, L. R. and P. R. Milgrom (1985): Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders. J. Finan. Econ. 14(1), 71-100.
22. Grossman, S. J., and M. H. Miller (1988): Liquidity and Market Structure. J. Finance 43(3), 617-637.
23. Guéant, O., and C.-A. Lehalle (2015): General Intensity Shapes in Optimal Portfolio Liquidation. Math. Finance 25(3), 457-495.
24. Guéant, O., C.-A. Lehalle, and J. Fernandez-Tapia (2012): Optimal Portfolio Liquidation with Limit Orders. SIAM J. Finan. Math. 3(1), 740-764.
25. Guilbaud, F., and H. Pham (2015): Optimal High-Frequency Trading in a Pro-rata Microstructure with Predictive Information. Math. Finance 25(3), 545-575.
26. Hanson, F. B. (2007): Applied Stochastic Processes and Control for Jump-diffusions: Modeling, Analysis, and Computation. Philadelphia: SIAM.
27. Hendershott, T., and H. Mendelson (2000): Crossing Networks and Dealer Markets: Competition and Performance. J. Finance 55(5), 2071-2115.
28. Horn, R. A., and C. R. Johnson (1985): Matrix Analysis. Cambridge: Cambridge University Press.
29. Höschler, M. (2011): Limit Order Book Models and Optimal Trading Strategies. PhD thesis, Technical University Berlin, 2011.
30. Huitema, R. (2012): Optimal Portfolio Execution Using Market and Limit Orders. Preprint. Available at: http://www.bf.uzh.ch/publikationen/pdf/3543.pdf. Accessed April 26, 2013.
31. Kallenberg, O. (2002): Foundations of Modern Probability. New York: Springer.
32. Klöck, F., A. Schied, and Y. Sun (2011): Existence and Absence of Price Manipulation in a Market Impact Model with Dark Pool. Preprint, 2012. Available at arXiv: http://arxiv.org/abs/1205.4008. Accessed April 26, 2013.
33. Kratz, P. (2011): Optimal Liquidation in Dark Pools in Discrete and Continuous Time. PhD thesis, Humboldt University Berlin.
34. Kratz, P. (2013): An Explicit Solution of a Non-linear Quadratic Constrained Stochastic Control Problem with an Application to Optimal Liquidation in Dark Pools with Adverse Selection. Preprint. Available at arXiv: http://arxiv.org/abs/1204.2498. Accessed April 26, 2013.
35. Kratz, P., and T. Schöneborn (2014): Optimal Liquidation in Dark Pools. Quant. Finance 14(9), 1519-1539.
36. Kyle, A. S. (1985): Continuous Auctions and Insider Trading. Econometrica 53(6), 1315-1336.
37. Laruelle, S., C.-A. Lehalle, and G. Pagès (2011): Optimal Split of Orders Across Liquidity Pools: A Stochastic Algorithm Approach. SIAM J. Finan. Math. 2(1), 1042-1076.
38. Mittal, H. (2008): Are You Playing in a Toxic Dark Pool? A Guide to Preventing Information Leakage. J. Trading 3(3), 20-33.
39. Naujokat, F., and N. Westray (2011): Curve Following in Illiquid Markets. Math. Finan. Econ. 4(4), 299-335.
40. Obizhaeva, A., and J. Wang (2013): Optimal Trading Strategy and Supply/Demand Dynamics. J. Finan. Markets 16(1), 1-32.
41. Øksendal, B. (2007): Stochastic Differential Equations: An Introduction with Applications. Berlin: Springer.
42. Øksendal, B., and Y. Hu (2008): Partial Information Linear Quadratic Control for Jump Diffusions. SIAM J. Control Optim. 47(4), 1744-1761.
43. Øksendal, B., and A. Sulem (2007): Applied Stochastic Control of Jump Diffusions. Berlin: Springer.
44. Reid, W. T. (1972): Riccati Differential Equations. New York: Academic Press.
45. Rogers, L. C. G., and S. Singh (2010): The Cost of Illiquidity and Its Effects on Hedging. Math. Finan. 20(4): 597-615.
46. Schied, A., and T. Schöneborn (2009): Risk Aversion and the Dynamics of Optimal Liquidation Strategies in Illiquid Markets. Finance Stochastics 13(2), 181-204.
47. Schied, A., T. Schöneborn, and M. Tehranchi (2010): Optimal Basket Liquidation for CARA Investors is Deterministic. Appl. Math. Finance 17(6): 471-489.
48. Schöneborn, T., and A. Schied (2009): Liquidation in the Face of Adversity: Stealth vs. Sunshine Trading. Preprint. Available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstractid=1007014. Accessed April 26, 2013.
49. Sofianos, G., and D. Jeria (2008a): Quantifying the Sigma X Crossing Benefit. Equity Execution Strategies: Street Smart 31, Goldman Sachs.
50. Sofianos, G., and D. Jeria (2008b): Quantifying the Sigma X Crossing Benefit: The Sequel. J. Trading 3(4), 84-91.
51. Ye, M. (2011): A Glimpse into the Dark: Price Formation, Transaction Costs, and Market Share in the Crossing Network. Preprint. Available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstractid=1521494. Accessed April 26, 2013.