  In this paper, we present a unified framework for decision making under
uncertainty. Our framework is based on the composite of two risk measures,
where the inner risk measure accounts for the risk of decision given the exact
distribution of uncertain model parameters, and the outer risk measure
quantifies the risk that occurs when estimating the parameters of distribution.
We show that the model is tractable under mild conditions. The framework is a
generalization of several existing models, including stochastic programming,
robust optimization, distributionally robust optimization, etc. Using this
framework, we study a few new models which imply probabilistic guarantees for
solutions and yield less conservative results comparing to traditional models.
Numerical experiments are performed on portfolio selection problems to
demonstrate the strength of our models.
