  A classical result in risk measure theory states that every coherent risk
measure has a dual representation as the supremum of certain expected value
over a risk envelope. We study this topic in more detail. The related issues
include: 1. Set operations of risk envelopes and how they change the risk
measures, 2. The structure of risk envelopes of popular risk measures, 3.
Aversity of risk measures and its impact to risk envelopes, and 4. A connection
between risk measures in stochastic optimization and uncertainty sets in robust
optimization.
