Portfolio Problems With Transaction Costs Under Short Sell Based On Two-Stage

Portfolio selection is one of the critical problems of finance theory. The main problem which portfolio solves is how to distribute some amount of capital into different kinds of assets to reduce the portfolio risk given specified expected return rate. The origin and the end of financial research can be thought in a certain way as portfolio selection which domains the investor's content of management and decision of finance. At present the existing models about portfolio do not consider transaction casts at most of the time, but in the actual investment activities, and each time when the transaction occurs, investors should pay the cost to the exchanges in accordance with the volume of transactions at a certain percentage. In this paper, we give a model of CVaR with transaction costs in stock market which allows short sell, but requires collateral.The foreword gives a brief introduction about the progress of the investment portfolio, the relevant theory about short sell, transaction costs and random programming.In Chapter 2, there list some preparatory knowledge mostly about the definition of CVaR and some of its characteristics widely used.Traditional two-stage stochastic programming considers the expectation as the preference criterion. However, the risk is presence while choosing the best decisions. In chapter 3, we give the specific portfolio model, pacify CVaR as the risk measure of two second phase of investment. The model is changed into a large scale linear programming by an auxiliary function substituting for the CVaR function and the linearity technique.In chapter 4, we give the specific portfolio model based on the model in chapter 3, first, we propose on two-stage portfolio problems with transaction costs, second we study portfolio problems with transaction costs under short sell based on two-stage. In the light of the specific stock dates, we get the best weight coefficient of portfolio with matlab. Based on the results, we execute numerical tests. The effect of expected return rate to the optimal policies is analyzed by changing expected return rate. Numerical tests also compare the impact of transaction costs and short sales to the portfolio investment.Results show that investors should select expected return rate and believe degree according to their risk preferences, while making investment decisions. Transaction costs play an important role to the market which allows short sell.