Journal of Systems Science and Complexity

, Volume 30, Issue 5, pp 1121–1135 | Cite as

An adaptive Lagrangian algorithm for optimal portfolio deleveraging with cross-impact

  • Fengmin XuEmail author
  • Min Sun
  • Yuhong Dai


This paper considers the problem of optimal portfolio deleveraging, which is a crucial problem in finance. Taking the permanent and temporary price cross-impact into account, the authors establish a quadratic program with box constraints and a singly quadratic constraint. Under some assumptions, the authors give an optimal trading priority and show that the optimal solution must be achieved when the quadratic constraint is active. Further, the authors propose an adaptive Lagrangian algorithm for the model, where a piecewise quadratic root-finding method is used to find the Lagrangian multiplier. The convergence of the algorithm is established. The authors also present some numerical results, which show the usefulness of the algorithm and validate the optimal trading priority.


Adaptive Lagrangian algorithm deleveraging price cross-impact 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Economics and FinanceXi’an Jiaotong UniversityXi’anChina
  2. 2.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina
  3. 3.The State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Science/Engineering Computing, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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