Worst-Case Distortion Risk Measure with Application to Robust Portfolio Selection

Portfolio selection depends heavily on the underlying distribution of loss. When the distribution information of loss can only be observed through a limited sample of data, robustness of the portfolio selection model is of crucial importance. Assuming that the underlying distribution of loss has a known mean and variance and lies within a ball centred on the reference distribution with the Wasserstein distance as the radius, this paper proposes a robust portfolio strategy model based on the distortion risk measure and translates it into a simpler equivalent form. Furthermore, simulation and empirical study are used to demonstrate the validity of the model.