Computing efficient frontiers using estimated parameters
Annals of Operations Research
Matrix computations (3rd ed.)
Regularization by Truncated Total Least Squares
SIAM Journal on Scientific Computing
Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
Mathematics of Operations Research
Robust Solutions to Uncertain Semidefinite Programs
SIAM Journal on Optimization
Robust portfolio selection problems
Mathematics of Operations Research
Operations Research
Perturbation of Sets and Centers
Journal of Global Optimization
Portfolio Selection with Robust Estimation
Operations Research
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
GloptiPoly 3: moments, optimization and semidefinite programming
Optimization Methods & Software - GLOBAL OPTIMIZATION
A Minimax Theorem with Applications to Machine Learning, Signal Processing, and Finance
SIAM Journal on Optimization
Robust portfolio selection based on a joint ellipsoidal uncertainty set
Optimization Methods & Software
A Hamilton-Jacobi-Bellman approach to optimal trade execution
Applied Numerical Mathematics
Optimal Portfolio Execution Strategies and Sensitivity to Price Impact Parameters
SIAM Journal on Optimization
Robust solutions of uncertain linear programs
Operations Research Letters
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An uncertainty set is a crucial component in robust optimization. Unfortunately, it is often unclear how to specify it precisely. Thus it is important to study sensitivity of the robust solution to variations in the uncertainty set, and to develop a method which improves stability of the robust solution. In this paper, to address these issues, we focus on uncertainty in the price impact parameters in an optimal portfolio execution problem. We first illustrate that a small variation in the uncertainty set may result in a large change in the robust solution. We then propose a regularized robust optimization formulation which yields a solution with a better stability property than the classical robust solution. In this approach, the uncertainty set is regularized through a regularization constraint, defined by a linear matrix inequality using the Hessian of the objective function and a regularization parameter. The regularized robust solution is then more stable with respect to variation in the uncertainty set specification, in addition to being more robust to estimation errors in the price impact parameters. The regularized robust optimal execution strategy can be computed by an efficient method based on convex optimization. Improvement in the stability of the robust solution is analyzed. We also study implications of the regularization on the optimal execution strategy and its corresponding execution cost. Through the regularization parameter, one can adjust the level of conservatism of the robust solution.