A Class Of Distributionnally Robust Optimization Problem Based On CVaR Model

Based on the mean-CVa R portfolio model,this paper considers a class of distributionally robust optimization problems.The robust optimization problem does not assume that the random variable obeys a specific distribution,but constructs a distribution set by the properties of its moment,limiting the first moment in a box uncertainty set,defining the upper bound of the second central moment.Under the premise of the above distribution,the objective function and constraints are transformed into the conic optimization problem,and then the conic optimization problem is transformed into the semidefinite programming(SDP)using Lagrange duality theory.The contents of this article can be summarized as follows:1.Chapter 1 introduces the form and research progress of distributionally robustoptimization problem,and the concrete form and equivalent form of CVa R model.2.Chapter 2 describes some basic knowledge of solving the problem of distributionallyrobust optimization,including the overview of robust optimization problem,Lagrangedual theory,SDP problem specific form and its solution method interior point method.3.Chapter 3 is the main part of this paper,we put forward the problem what we want tosolve,give the concrete form of uncertainty set,and complete the transformation toSDP problem.4.Chapter 4 is numerical experiments.With the YALMIP package in MATLAB,thestochastic data experiments is used to verify the solvability of the model.Then,basedon historical data in real market,we explore the return of the model.