The CVaR Analysis Based On Worst-case With Application In Generation Asset Allocation

Portfolios theory is one of the important research contents in Economics. It aims to attain the portfolios of the maximum of the investment's return with the given value of the risk of portfolios or of the minimum of investment's risk with the given level of the investment's return. Based on the concept of the worst-case conditional value-at-risk (WCVaR), this paper presents three profit-risk robust portfolio models. Furthermore, the characteristic and calculation method of this new model is investigated. The primary contents are as follows:In the first section, we mainly introduce Lagrangian duality theory and some very important theory about risk measurement and management. On the foundation of the definition of CVaR described and the methods of applying CVaR decision are analysed. In addition, our research works of this paper are also briefly introduced.In the second section, we mainly introduce the definition of WCVaR. We discuss some very important theory about distribution uncertainty(such as mixture distribution uncertainty and discrete distribution). We analysis WCVaR model under the mixture distribution uncertainty and discrete distribution.In the third section, under the box discrete distribution of random variables, we present three profit-risk robust portfolio models, which are composed of min-max-type optimization problems. With the linear loss function, the proposed models are facilitated equivalently. Furthermore, we reduce the reformulations to linear programming problems. The relationship of solutions between the proposed models and the reduced ones is proved, which shows that by solving the reduced models, we can obtain the solutions of the original problems. As an example with power markets, Numerical simulations are done to test the models and the approach.In the fourth section, we analysis three profit-risk robust portfolio models under the compoud distribution of random variables. The proposed models are reduced to linear programming problems and we proved the relationship of solutions between the proposed models and the reduced ones. By using the numerical simulation approach, we analysis risk-profit and give efficient frontier of portfolio.In the fifth section, we summarize our work in this paper and introduce our next research.