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We investigate the optimal portfolio deleveraging (OPD) problem withpermanent and temporary price impacts, where the objective is to maximizeequity while meeting a prescribed debt/equity requirement. We take the realsituation with cross impact among different assets into consideration. Theresulting problem is, however, a non-convex quadratic program with a quadraticconstraint and a box constraint, which is known to be NP-hard. In this paper,we first develop a successive convex optimization (SCO) approach for solvingthe OPD problem and show that the SCO algorithm converges to a KKT point of itstransformed problem. Second, we propose an effective global algorithm for theOPD problem, which integrates the SCO method, simple convex relaxation and abranch-and-bound framework, to identify a global optimal solution to the OPDproblem within a pre-specified $\epsilon$-tolerance. We establish the globalconvergence of our algorithm and estimate its complexity. We also conductnumerical experiments to demonstrate the effectiveness of our proposedalgorithms with both the real data and the randomly generated medium- andlarge-scale OPD problem instances.

Effective Algorithms for Optimal Portfolio Deleveraging Problem with Cross Impact