Optimal liquidation of financial derivatives

We propose a two-period robust optimization model for portfolio liquidation under a cash requirement that finds the least costly liquidation strategy. The basic asset return is assumed to belong to a scaled ellipsoid while the derivative return is modeled as a quadratic function of the underlying asset return via delta-gamma approximation. We show that the robust liquidation model is equivalent to a computationally tractable semidefinite program. We obtain analytical properties regarding how derivative Greek letters affect the optimal liquidation strategy.