Robust Optimization Theory With Application To The Portfolio Selection Problems Under The (p,w)-norm Uncertainty

Robust optimization is a effective tool to solve the uncertain optimization problem, which is widely used in science, engineering science, economics, management and many other fields, involving the securities portfolio optimization, internet topology structure design, adaptive design, engineering design, impact resistance ability of the social system, supply chain management research, and so on. Uncertain set is the most important factor in robust optimization theory. The model often can get different objective function values under different uncertainties, and we always estimate a model from the tradeoff between optimality and robustness. In recent years, robust optimization has great effect from the initial portfolio problem to the portfolio with value at risk and the conditional value at risk portfolio problems, etc. Due to its robustness, which has anti-interference role and can resist many uncertain factors of the outside world, investors can use it to cope with the complex financial environment. Attracted by this, in this dissertation, first a new uncertain set-(p,w)-norm has been proposed, for the reason not only to make up the disadvantages of "the uncertain parameters of all possible values will give the same weight", but also to consider the robust cost of the robust optimization model. Next, we discuss the (p,w)-norm uncertain set and its robust counterpart and the probabilistic guarantees, etc. Finally, we give a numerical example about a portfolio selection problem and the empirical results show that the D-norm is a special case of (p,w)-norm and the value of the objective function under the D-norm sometimes is not as optimal as the value under the (p,w)-norm, though both their solutions have diversities. In conclusion, we summarize this dissertation and give some corresponding outlook.