Mean–variance portfolio optimization with parameter sensitivity control
MetadataShow full item record
The mean–variance (MV) portfolio selection model, which aims to maximize the expected return while minimizing the risk measured by the variance, has been studied extensively in the literature and regarded as a powerful guiding principle in investment practice. Recognizing the importance to reduce the impact of parameter estimation error on the optimal portfolio strategy, we integrate a set of parameter sensitivity constraints into the traditional MV model, which can also be interpreted as a model with marginal risk control on assets. The resulted optimization framework is a quadratic programming problem with non-convex quadratic constraints. By exploiting the special structure of the non-convex constraints, we propose a convex quadratic programming relaxation and develop a branch-and-bound global optimization algorithm. A significant feature of our algorithm is its special branching rule applied to the imposed auxiliary variables, which are of lower dimension than the original decision variables. Our simulation analysis and empirical test demonstrate the pros and cons of the proposed MV model with sensitivity control and indicate the cases where sensitivity control is necessary and beneficial. Our branch-and-bound procedure is shown to be favourable in computational efficiency compared with the commercial global optimization software BARON.
This is an Author's Original Manuscript of an article published by Taylor & Francis in Optimization Methods and Software on 16/05/2016 available online at http://www.tandfonline.com/doi/full/10.1080/10556788.2016.1181758
Showing items related by title, author, creator and subject.
Liew, Emily Wan Teng (2011)Mixing plays a substantial role in determining the overall performance of a bioreactor. Well mixing in bioreactor, especially for ethanolic fermentation process is important for the homogenization of miscible and immiscible ...
Loxton, Ryan Christopher (2010)In this thesis, we develop numerical methods for solving five nonstandard optimal control problems. The main idea of each method is to reformulate the optimal control problem as, or approximate it by, a nonlinear programming ...
Al Helal, Z.; Rehbock, Volker; Loxton, Ryan (2015)Regulating the blood glucose level is a challenging control problem for the human body. Abnormal blood glucose levels can cause serious health problems over time, including diabetes. Although several mathematical models ...