We derive an explicit solution for deterministic market impact parameters in the Graewe and Horst (2017) portfolio liquidation model. The model allows to combine various forms of market impact, namely instantaneous, permanent and temporary. We show that the solutions to the two benchmark models of Almgren and Chriss (2001) and of Obizhaeva and Wang (2013) are obtained as special cases. We relate the different forms of market impact to the microstructure of limit order book markets and show how the impact parameters can be estimated from public market data. We investigate the numerical performance of the derived optimal trading strategy based on high frequency limit order books of 100 NASDAQ stocks that represent a range of market impact profiles. It shows the strategy achieves significant cost savings compared to the benchmark models of Almgren and Chriss (2001) and Obizhaeva and Wang (2013) .
SUMMARYNon-associated flow rule is essential when the popular Mohr-Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes nonsymmetric when this non-associated flow rule is applied. Efficient solution of this large-scale nonsymmetric linear system is of practical importance. The standard Krylov solver for a non-symmetric solver is Bi-CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s = 6) is more efficient than Bi-CGSTAB when the preconditioner is the incomplete factorization with zero fill-in of global stiffness matrix K ep (ILU(0)-K ep ). Iteration time is reduced by 40% by using IDR(s = 6) with ILU(0)-K ep . To further reduce computational cost, the global stiffness matrix K ep is divided into two parts. The first part is the linear elastic stiffness matrix K e , which is formed only once at the beginning of solution step. The second part is a low-rank matrix Δ, which is re-formed at each Newton-Raphson iteration. Numerical studies show that IDR(s = 6) with this ILU(0)-K e preconditioner is more time effective than IDR(s = 6) with ILU(0)-K ep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used.
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