The Research On Uncertain Portfolio Optimization Problem With Chance Constraint

With the improvement of various kinds of financial system in China,the investment channels showed diversified development.However,due to the influence of uncertain factors such as policy revision,market change,enterprise management and so on,how to choose an optimal investment mode to balance the proportion requirement of risks and benefits has become the focus of investors,the selection method of portfolio can provide important basis for decision making of investment.Based on the uncertainty of various factors in reality,the model of related portfolio problem under random condition was given.In order to deal with the objective function of initial problem effectively,the objective function was transformed into the expectation form by using the distribution of random variable.Thus the related optimization problem to be addressed was obtained in the following form Where,(?)The above model was handled by two different methods,then the original problem was converted into an equivalent form,which was easier to deal with.One of the processing method,which under the condition that some moment information about the random variable was known,was to describe the uncertain distribution set with the known moment information.The initial chance constraint was handled by robust method,thus the distributionally robust chance constraint was obtained.Then through the introduction of Conditional Value at Risk(CVaR)to represent distributionally robust chance constraint approximately,the Worst-Case CVaR approximation was given and its accuracy was shown,and the objective function was handled,thus an equivalent model of above optimization problem was obtained.The other method,which under the condition that the empirical distribution about the random variable was known,was to construct the uncertain distribution set with the modified ?2-divergence distance between the empirical distribution and unknown distribution.And the problem of uncertain parameter to unknown distribution was transformed into convex optimization problem of likelihood ratio to known empirical distribution by measure theory,and then the equivalent form of corresponding optimization problem was obtained by using the Lagrange duality theory.