A Pivoting Method For The Portfolio Decision Under The Condition Of Not Allowing Short Sales

In this paper, it is discussed that the portfilio model can charge into Linear complementarity problem using Kucker-Tucker theorem, and we propose a pivoting method and present a method to solve the high-dimension portfolio problem. We also make some computationalExperimence .Our computing illustrates that our methods are efficient and reliable , which can help the investor make decision in practice. An advantage of this method is that it can be applied when the covariance matrix of the invested projects is positive semi-definite.In Ⅰ,it is discussed how to estimate the profit expection and risk of portfolio by time series, and that the portfolio investment model can be made by the variance of portfolio selection random profit.In Ⅱ, we obtain the optimality conditions for quadratic programming—Linear complementarity problem by Kuhn-Tucker theorem.In Ⅲ, first a pivoting method for linear complementarity problem can be proposed by its feature and the simplex algorithm for Linear programming. Second we give copositive-plus matrix and invest the finite convergence analysis.In Ⅳ, we present the pivoting method to solve the portfolio selection model, and also show some computational experimence by C program.The result of numerical experiment is satisfactory.