Abstract: In this paper, we consider a two-period financial derivative liquidation problem without the convexity assumption. Its optimization model is a non-convex quadratic programming problem with a single quadratic constraint and linear constraints, which is NP-hard. We propose a faster new semi-definite programming (SDP) relaxation for this model by making use of its special structure, and estimate the gap between it and the original problem. We also show that it provides a tighter lower bound than the existing SDP relaxation in the literature. Numerical experiments show that this SDP relaxation can fast provide a very tight lower bound for the original problem, thus can provide effective lower bounds in branch-and-bound algorithm to find the global optimal solution of the problem.

Key words: financial optimization, two-period financial derivative liquidation problem, non-convex QCQP, SDP relaxation