Optimization Models And Algorithms In Portfolio Selection Problem

This dissertation studies optimization models and algorithms in portfolio selection problem. First, the mean-variance model proposed by Markowitz is introduced. And what's more, some related ideas and principles are summarized. Finally, we mainly investigate the following three problems:(1) The problem of portfolio selection with transaction costs is formulated as a bi-objective programming model, but it is no-differentiable and difficult to solve. With a transformation, we can transform the nondifferentiable nonlinear programming problem to a linear program. We propose a new method to make this process much simpler and it also can reduce the number of the variables of the final linear program.(2) We consider a minimax model for optimal portfolio selection at the situation that the return rates of risky assets can not be precisely estimated. We introduce transaction costs into the minimax model and derive the analytical expressions of an optimal portfolio and the frontier portfolios. (3) We consider a financial market model with frictions which include transaction costs, bid-ask spread and taxes. By using optimization techniques, several necessary and sufficient conditions are derived for the weak no-arbitrage in both single period and multi-period model.