Robust Optimization Of The Robust Portfolio

The research object of this paper is the problem of portfolio selection, and the most classic portfolio theory is Markowitz’s mean-variance model.As in mean-variance model, small changes of the expected return will produce greater effect on asset allocation problem,the model is lack of robustness. As a result, this paper takes robust portfolio problem into account. On this basis, we consider uncertainty of the constraint coefficients, and get the stochastic pro-gramming model of the robust portfolio.First this paper considers the market risk-free assets, and assumes there are L risk assets on the market.in short sales situation, model without no risk-free asset can be expressed as follows: Where ai∈RL,i=I,…,n are the uncertain amounts,denotes the income vector under the influence of the i impact factor. vi,i=1,…, n are known quantities, represent investors’earnings targets When the uncertain income of financial assets is ai. Because products in the capital market are colorful, and there are a wide variety of assets available for investment, the paper consider the existence of the risk-free asset market in order to be closer to the reali-ty. The robust portfolio model with no risk-free asset is given. Though risk measure methods are diverse,VaR and CVaR are widely used and are regarded as the basic risk measure methods by financial institutions. VaR and CVaR can represent the size of market risk more intuitive, and quantify and limit losses.So this paper will also consider the stochastic robust portfolio models based on VaR and CVaR.Since the consideration of income uncertainty, the robust portfolio models for this paper are stochastic programming. Traditional stochastic program-ming methods need to know the probability distribution of random variables, which are often difficult to achieve, and the results are sensitive to uncertain-ty. Robust optimization method is a very effective way for studying the issue of uncertainty, and successfully understand the sensitive issues of uncertainty and docs not need to know the specific distribution of the random variables. This paper analyze four robust portfolio models with the robust optimiza-tion method, considering the uncertain sets in aggregate form, and represents uncertainties of the data dependent on an group of independent random vari-ables, gets the robust counterparts. The original problems are transformed into linear programmings or SOCP, so problems are easy to calculate, and the solutions are robust.In the empirical part,this paper analysis securities in hot plates in the Shanghai Stock Exchange, and realize the computation of the robust coun-terpart by R statistical software and Matlab.Finally,this paper compare the solutions got by robust optimization with these which we get by the tradition-al solutions, and verify the stability and effectiveness of solutions got by the robust method.