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

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Abstract

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.

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Author information

Authors and Affiliations

  1. School of Economics and Finance, Xi’an Jiaotong University, Xi’an, 710049, China

    Fengmin Xu

  2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Min Sun

  3. The State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Science/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yuhong Dai

Authors
  1. Fengmin Xu
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  2. Min Sun
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  3. Yuhong Dai
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Corresponding author

Correspondence to Fengmin Xu.

Additional information

This work was supported by the Chinese Natural Science Foundation under Grant Nos. 11571271, 11331012, 71331001, 11631013, the National Funds for Distinguished Young Scientists under Grant No. 11125107 and the National 973 Program of China under Grant No. 2015CB856000.

This paper was recommended for publication by Editor WANG Shouyang.

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Xu, F., Sun, M. & Dai, Y. An adaptive Lagrangian algorithm for optimal portfolio deleveraging with cross-impact. J Syst Sci Complex 30, 1121–1135 (2017). https://doi.org/10.1007/s11424-017-5299-1

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  • DOI: https://doi.org/10.1007/s11424-017-5299-1

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