  The paper investigates the robust optimized certainty equivalents and
analyzes the relevant properties of them as risk measures for loss positions
with distribution uncertainty. On this basis, the robust generalized quantiles
are proposed and discussed. The robust expectiles with two specific
penalization functions $\varphi_{1}$ and $\varphi_{2}$ are further considered
respectively. The robust expectiles with $\varphi_{1}$ are proved to be
coherent risk measures, and the dual representation theorems are established.
In addition, the effect of penalization functions on the robust expectiles and
its comparison with expectiles are examined and simulated numerically.
