An adaptive Lagrangian algorithm for optimal portfolio deleveraging with cross-impact
- 116 Downloads
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.
KeywordsAdaptive Lagrangian algorithm deleveraging price cross-impact
Unable to display preview. Download preview PDF.
- Scholes M S, Crisis and risk management, American Economic Review, 2000, 17–21.Google Scholar
- Sias R W, Starks L T, and Titman S, The price impact of institutional trading, Available at SSRN 283779, 2001.Google Scholar
- Xu F, Zhao Z, and Dai Y H, Behavior analysis and high performance algorithm for optimal portfolio liquidation with market impact, Technical Report, Xi’an Jiaotong University, 2015.Google Scholar
- Gong P, Zhang C, Lu Z, et al., A general iterative shrinkage and thresholding algorithm for nonconvex regularized optimization problems, Machine Learning: Proceedings of the International Conference, International Conference on Machine Learning, NIH Public Access, 2013, 28(2): 37.Google Scholar