TY - JOUR
T1 - Regularized robust optimization
T2 - The optimal portfolio execution case
AU - Moazeni, Somayeh
AU - Coleman, Thomas F.
AU - Li, Yuying
PY - 2013/6
Y1 - 2013/6
N2 - 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.
AB - 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.
KW - Estimation errors
KW - Portfolio optimization
KW - Price impact
KW - Robust optimization
UR - http://www.scopus.com/inward/record.url?scp=84877732179&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84877732179&partnerID=8YFLogxK
U2 - 10.1007/s10589-012-9526-3
DO - 10.1007/s10589-012-9526-3
M3 - Article
AN - SCOPUS:84877732179
SN - 0926-6003
VL - 55
SP - 341
EP - 377
JO - Computational Optimization and Applications
JF - Computational Optimization and Applications
IS - 2
ER -