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When to Cross the Spread: Curve Following with Singular Control

  • Felix Naujokat
  • Ulrich Horst

In this article the problem of curve following in an illiquid market is addressed. Using techniques of singular stochastic control, we extend the results of [NW11] to a twosided limit order market with temporary market impact and resilience, where the bid ask spread is now also controlled. We first show existence and uniqueness of an optimal control. In a second step, a suitable version of the stochastic maximum principle is derived which yields a characterisation of the optimal trading strategy in terms of a nonstandard coupled FBSDE. We show that the optimal control can be characterised via buy, sell and no-trade regions. The new feature is that we now get a nondegenerate no-trade region, which implies that market orders are only used when the spread is small. This allows to describe precisely when it is optimal to cross the bid ask spread, which is a fundamental problem of algorithmic trading. We also show that the controlled system can be described in terms of a reflected BSDE. As an application, we solve the portfolio liquidation problem with passive orders.

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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2011-053.

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Length: 31 pages
Date of creation: Aug 2011
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2011-053
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  1. Raffaele Fiocco & Carlo Scarpa, 2011. "The Regulation of Interdependent Markets," SFB 649 Discussion Papers SFB649DP2011-046, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Kartik Anand & Prasanna Gai & Matteo Marsili, 2011. "Rollover risk, network structure and systemic financial crises," SFB 649 Discussion Papers SFB649DP2011-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Wolfgang Karl Härdle & Brenda López Cabrera & Ostap Okhrin & Weining Wang, 2011. "Localising temperature risk," SFB 649 Discussion Papers SFB649DP2011-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Stephan Stahlschmidt & Helmut Tausendteufel & Wolfgang K. Härdle, 2011. "Bayesian Networks and Sex-related Homicides," SFB 649 Discussion Papers SFB649DP2011-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Alexander Meyer-Gohde, 2011. "Monetary Policy, Determinacy, and the Natural Rate Hypothesis," SFB 649 Discussion Papers SFB649DP2011-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Juliane Scheffel, 2011. "How do Unusual Working Schedules Affect Social Life?," SFB 649 Discussion Papers SFB649DP2011-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  7. Raffaele Fiocco & Mario Gilli, 2011. "Bargaining and Collusion in a Regulatory Model," SFB 649 Discussion Papers SFB649DP2011-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Johanna Kappus & Markus Reiß, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers SFB649DP2010-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  9. Fehr, Dietmar & Schmid, Julia, 2014. "Exclusion in the all-pay auction: An experimental investigation," Discussion Papers, Research Unit: Market Behavior SP II 2014-206, Social Science Research Center Berlin (WZB).
  10. Gunda-Alexandra Detmers & Dieter Nautz, 2012. "The Information Content of Central Bank Interest Rate Projections: Evidence from New Zealand," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 323-329, 09.
  11. Anand, Kartik & Gai, Prasanna & Kapadia, Sujit & Brennan, Simon & Willison, Matthew, 2013. "A network model of financial system resilience," Journal of Economic Behavior & Organization, Elsevier, vol. 85(C), pages 219-235.
  12. Schied, Alexander & Schoeneborn, Torsten, 2008. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," MPRA Paper 7105, University Library of Munich, Germany.
  13. Alexander Meyer-Gohde, 2011. "Sticky Information and Determinacy," SFB 649 Discussion Papers SFB649DP2011-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  14. Esra Akdeniz Duran & Wolfgang Karl Härdle & Maria Osipenko, 2011. "Difference based Ridge and Liu type Estimators in Semiparametric Regression Models," SFB 649 Discussion Papers SFB649DP2011-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  15. Beresford, Alastair R. & Kübler, Dorothea & Preibusch, Sören, 2010. "Unwillingness to pay for privacy: A field experiment," Discussion Papers, Research Unit: Market Behavior SP II 2010-03, Social Science Research Center Berlin (WZB).
  16. Lydia Mechtenberg & Johannes Münster, 2011. "A strategic mediator who is biased into the same direction as the expert can improve information transmission," SFB 649 Discussion Papers SFB649DP2011-012, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  17. Heike Belitz & Marius Clemens & Christian von Hirschhausen & Jens Schmidt-Ehmcke & Axel Werwatz & Petra Zloczysti, 2011. "An Indicator for National Systems of Innovation: Methodology and Application to 17 Industrialized Countries," Discussion Papers of DIW Berlin 1129, DIW Berlin, German Institute for Economic Research.
  18. Markus Reiß & Yves Rozenholc & Charles A. Cuenod, 2011. "Pointwise adaptive estimation for quantile regression," SFB 649 Discussion Papers SFB649DP2011-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  19. Till Strohsal & Enzo Weber, 2011. "Mean-Variance Cointegration and the Expectations Hypothesis," SFB 649 Discussion Papers SFB649DP2011-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  20. Dirk Hofmann & Salmai Qari, 2011. "The Law of Attraction: Bilateral Search and Horizontal Heterogeneity," SFB 649 Discussion Papers SFB649DP2011-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  21. Juliane Scheffel, 2011. "Identifying the Effect of Temporal Work Flexibility on Parental Time with Children," SFB 649 Discussion Papers SFB649DP2011-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  22. Lu Lin & Feng Li & Lixing Zhu & Wolfgang Karl Härdle, 2011. "Mean Volatility Regressions," SFB 649 Discussion Papers SFB649DP2011-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  23. Xiaoliang Liu & Wei Xu & Martin Odening, 2011. "Can crop yield risk be globally diversified?," SFB 649 Discussion Papers SFB649DP2011-018, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  24. Wolfgang Karl Härdle & Vladimir Spokoiny & Weining Wang, 2011. "Local Quantile Regression," SFB 649 Discussion Papers SFB649DP2011-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  25. Wolfgang Karl Härdle & Maria Osipenko, 2011. "Spatial Risk Premium on Weather Derivatives and Hedging Weather Exposure in Electricity," SFB 649 Discussion Papers SFB649DP2011-013, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  26. Sigbert Klinke, 2011. "Developing web-based tools for the teaching of statistics: Our Wikis and the German Wikipedia," SFB 649 Discussion Papers SFB649DP2011-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  27. Rong Liu & Lijian Yang & Wolfgang Karl Härdle, 2011. "Oracally Efficient Two-Step Estimation of Generalized Additive Model," SFB 649 Discussion Papers SFB649DP2011-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  28. Markus Reiß, 2011. "Asymptotic equivalence and sufficiency for volatility estimation under microstructure noise," SFB 649 Discussion Papers SFB649DP2011-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  29. Esra Akdeniz Duran & Mengmeng Guo & Wolfgang Karl Härdle, 2011. "A Confidence Corridor for Expectile Functions," SFB 649 Discussion Papers SFB649DP2011-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  30. Shuzhuan Zheng & Lijian Yang & Wolfgang Karl Härdle, 2011. "A Confidence Corridor for Sparse Longitudinal Data Curves," SFB 649 Discussion Papers SFB649DP2011-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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