The Convergence Of Conditional Value-at-risk

With the development of mathematical model, many researchers pay much more attention to the stochastic optimization model. It is difficult for people to solve a stochastic optimization model directly. And the study of deterministic optimization models has been a series of good research results. So people pay close attention to transform a stochastic optimization model to a deterministic optimization model and the stochastic optimization model is uniform convergence to the deterministic optimization model. Besides the solution set of these optimization models are uniform convergence.The main content in this paper is followed:In the second chapter, we first introduce the basic definitions and lemmas which are used to proof and explain the theories involved in my paper. Thus we can understand this paper well.In the third chapter, we proof the uniform convergence of stochastic inequality constraint sets and equality constraint sets with SAA method. On this basis, we proof the uniform conver-gence of the solution sets of the stochastic optimization models. At the same time we proof that the solution sets of CVaR are uniform convergence.In the forth chapter, we transform a model of CVaR to a nonconvex and nonsmooth opti-mization model. Then a appropriate algorithm is given. Computational results using two stock selection problems with a CVaR constraint are presented.