We present a new approach for portfolio selection when the underlying distribution of asset returns is uncertain or ambiguous to investors. In particular, we consider the case that an investor can formulate some reference financial models based on his/her prior beliefs or information, but is concerned about misspecification of the reference models and the associated loss. Based on the concept of Distributionally Robust Optimization (DRO), we introduce a new penalty framework that provides investors flexibility to define prior reference models using moment information and accounts for model ambiguity in terms of moment uncertainty. In particular, our approach enables an investor to optimize his/her portfolio while seeking a balance between relying on knowledge of reference models and taking into account possible ambiguity of the models. We further provide efficient solution methods for the penalized moment-based problem. Computational experiments show that our penalized moment-based approach outperforms classical DRO approaches in many cases. Furthermore, the approach can be extended to incorporate alternative uncertainty structures and factor models.
Submitted to Journal. October, 2010.