Worst-case CVaR Optimization In Two-stage Problem With Application In Power Market

Portfolios theory is one of the important research topic in Economics. It is designed to attain the portfolios of the maximum of the investment's return with the expected value of the risk range of portfolios or of the minimum of investment's risk with the expected level of the investment's return. Based on the concept of WCVaR (Worst-case Conditional Value-at-Risk), this paper builds a two-stage of WCVaR profit-risk robust portfolio model. Under the discrete box distribution of random variable, the calculation method and characteristic of the model are analyzed. Meanwhile, it's applied to asset allocation of electric market related problems. The primary contents are as follows:In the first chapter, we mainly present the background and the significance. This chapter makes a detail about the current domestic and international related research situation of the two-stage problem in profit-risk robust. Meanwhile, we introduce three kinds of optimization models in power market and the Lagrangian duality theory, put forward the research innovation and arrangement of this paper.In the second chapter, we mainly introduce the current risk measurement method and compare the different methods. We analyse WCVaR risk-profit optimization model under the two-time periods. It makes the foundation for next chapter.In the third chapter, Based on the single period WCVaR model, we present a two-stage of WCVaR profit-risk portfolio model and a two-stage of WCVaR portfolio model which calculates by expectation under the discrete box distribution of random variables. This new models are composed of multi-layer min-max structure and high-dimension optimization problems. Assuming the loss function is linear, the proposed models are further reduced equivalently to simple linear programming problems by the Lagrange duality theory.The fourth chapter applies the proposed models to power asset allocation problem by Monte-Carlo simulation. The results show the effectiveness of the models in theory. The study has important guiding significance and the practical application value for investors, and provides new ideas for power suppliers'portfolio , risk analysis and risk management.The last chapter summarizes and makes the final conclusion of this paper. We also point out some directions of the further study.