The Study On Globalized Distributionally Robust Portfolio Optimization Problem Based On Wasserstein Metric

In practical problems of portfolio optimization,the rate of return on assets is uncertain under the infuence of various factors.In order to provide a better decision plan and measure investment risk,we need to study how to take uncertain rate of return into portfolio optimization.Robust optimization is a popular method to deal with uncertain parameters in a model.When an uncertain parameter is viewed as a random variable with an unknown distribution,an important way to deal with ambiguity in parameter distribution information is distributionally robust optimization(DRO).One unavoidable problem,however,is that the optimal solution to DRO is very conservative,because DRO takes the worst case in an ambiguity that includes all possible distributions.A simple approach is to reduce the distribution ambiguity,but this approach does not solve the problem because the true distribution may be detached from the selected ambiguity.Then,in the DRO problem,we can also introduce a global method to reduce the conservativeness of DRO and relax the feasibility requirements of ambiguity.Based on Wasserstein metric and the strong duality theorem of linear cone,this dissertation transforms the globalized distributionally robust optimization problem with uncertain distribution into the globalized distributionally robust optimization counterpart with deterministic distribution.We apply the globalized distributionally robust optimization model to the CVa R portfolio problem,and construct a globalized distributionally optimization portfolio problem.Through model transformation,we obtain the globalized distributionally robust portfolio counterpart under deterministic distribution.Finally,numerical simulation is carried out to prove the feasibility of the model,and the comparison of the models shows that the model is efective in reducing the conservativeness of the model,and has certain guidance for investment decision.