Effective algorithms for optimal portfolio deleveraging problem with cross impact

We investigate the optimal portfolio deleveraging (OPD) problem with permanent and temporary price impacts, where objective is to maximize equity while meeting a prescribed debt/equity requirement. take real situation cross impact among different assets into consideration. The resulting is, however, nonconvex quadratic program constraint box constraint, which known be NP-hard. In this paper, we first develop successive convex optimization (SCO) approach for solving OPD show that SCO algorithm converges KKT point of its transformed problem. Second, propose an effective global problem, integrates method, simple relaxation, branch-and-bound framework, identify solution within prespecified ε-tolerance. establish convergence our estimate complexity. also conduct numerical experiments demonstrate effectiveness proposed algorithms both data randomly generated medium- large-scale instances.