The Study, Based On The Generalized Cvar Portfolio

The CVaR method is concerned by the society more and more. But this method will display ill-posedness in the certain circumstances. Recently, this problem already was realized by the economical world and the industrial world. And it becomes the hot research topic now. Therefore, alleviating the CVaR technology's ill-posedness not only has the theory significance, but also has the economic value. In the existing research foundation, this article plans to continue to discuss CVaR's ill-posedness, and obtains some meaningful results.Regarding big scale investment portfolio choice problems, this article uses the penalty function method to analyze the portfolio choice problems based on CVaR, and obtains a continuous solution with respect to the parameter. Meanwhile, it shows that the ill-posedness of solutions is alleviated by an example.After that, based on the CVaR optimization model with transaction costs, we simulate smoothly the piecewise linear function in objective function separately, and obtain the continuous smooth CVaR optimization model. As an application, we explain via an example when the smooth simulation model is applied in the big scale investment portfolio choice problems, its convergence and stability has the enhancement comparing with the above linear model.Finally, in the setting of the small scale transaction, this article establishes the new CVaR optimization model with concave cost functions, and arrives at the iterative method to solve the model. The author also analyzes the solution's stability of this model briefly.