Robust Optimal Portfolio In Uncertain Markets

The mean-variance methodology for the portfolio selection problem originally proposed by Markowitz, has been one of the most important research fields in modern finance theory. But the model must assume that the expected returns of the risky and risk-free assets as well as the covariance matrix of the risky assets are exactly known, it's well known that the asset return forecasts and risk estimates are inherently inaccurate. In this paper we assume the expected returns of the risky and risk-free assets as well as the covariance matrix of the risky assets are not exactly known, but defined by some known elements, which form the vertices of this polytope. Robust optimal portfolio problems are proposed in the market with and without risk-free asset. And the analytical solutions are given out when the covariance matrix of the risky assets are exactly known. This paper consists of the following four chapters:In the first chapter we introduce the development of portfolio theory, and the development of robust portfolio theory, show that the expected returns of the risky and risk-free assets as well as the covariance matrix of the risky assets are exactly known in classical Markowitz mean-variance model. But it's well known that asset return forecasts and risk estimates are inherently inaccurate.In the second chapter, we introduce the solutions of the Markowitz's mean-variance model in the market with and without risk-free asset, and introduce robust optimal portfolio model.In the third chapter, we assume the expected returns of the risky and risk-free assets as well as the covariance matrix of the risky assets are not exactly known, but defined by some known elements, which form the vertices of this polytope. We consider three problems, the first one is when there exists no risk-free asset in the...