An Adaptive Lagrangian Algorithm for Optimal Portfolio Deleveraging with Cross-Impact  

作　　者：XU Fengmin SUN Min DAI Yuhong 

机构地区：[1]School of Economics and Finance,Xi'an Jiaotong University,Xi'an 710049,China [2]School of Mathematics and Statistics,Xi'an Jiaotong University,Xi'an 710049,China [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

出　　处：《Journal of Systems Science & Complexity》2017年第5期1121-1135,共15页系统科学与复杂性学报（英文版）

基　　金：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;the National 973 Program of China under Grant No.2015CB856000

摘　　要：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.

关 键 词：Adaptive Lagrangian algorithm deleveraging price cross-impact 

分 类 号：F224[经济管理—国民经济] F830.9