Research Of Algorithms Of CVaR Reward-Risk Ratio Problems

Both the measure methods and the coordination of reward and risk are the mostimportant topics in the portfolio selection problems. Ratio optimization model is aclass of optimization model which is used to balance the relationship between rewardand risk. Based on the concept of WCVaR(Worst-case Conditional Value-at-Risk), thispaper considers the ratio of reward-risk optimization models under the uncertaintydistribution. The main job of this paper are as follows: (i) This paper analyses theratio optimization model under uncertainty information.(ii) This paper introduces cutplane method and level function method to solve the model in paper. New methodsplay a special role in solving large-scale problems due to its simplicity and very lowmemory requirement. The whole paper is divided five chapters.In the first section, we mainly introduce a detailed summary about historicalbackground of risk management methods and current research of optimization modelat home and abroad. This chapter also presents some typical number computationapproaches about the solution in these models.In the second section, the worst-case ratio optimization model is introduced, andthe original model can be converted to its equivalent by duality theory undercomposite mixture distribution, and this chapter also analyze the properties of themodel.In the third section, the fundamental ideal of cut plane method and itsbackground are introduced. We deal with nonsmooth factor in the model and wenotice that the model has a special structure after equivalent transformation, and solveit by cut plane method. Cut plane method is confirmed to be feasibility and hasadvantage for solving large-scale problems due to its very low memory requirementcomparing with linear programming algorithm in numerical examples.In the fourth section, we introduce the fundamental ideal of level functionmethod which is first presented for solving stochastic dominance. As a tentativeapplication to the solution of this model, we move the nonsmooth constraints to theobjective by a penalty function. Then we use level function method to solve the iterative solution. Lastly level function method is confirmed to be feasibility innumerical examples.In the fifth section, we summarize the study, and give some suggestions forfurther study.