The semi-definite programming relaxation method for two-period financial derivatives'liquidation problem
The semi-definite programming(SDP)relaxation method for two-period financial derivatives'liquidation problem is studied without restricting the relationship between the magnitude of the temporary and permanent price impact parameters,and the optimization model is a nonconvex quadratically constrained quadratic programming(QCQP)problem with linear and single nonconvex quadratic constraints.An SDP relaxation with secant cuts for this nonconvex QCQP problem is presented and the gap between it and the original problem is estimated.The numerical results of random instances show that the SDP relaxation can obtain a tighter upper bound to the original problem and then provides a method for finding a good approximate solution to the problem.
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