  In this paper, we discuss the ambiguous chance constrained based portfolio
optimization problems, in which the perturbations associated with the input
parameters are stochastic in nature, but their distributions are not known
precisely. We consider two different families of perturbation distributions --
one is when only upper & lower bounds of mean values are known to us, and the
second one is along with the mean bounds, we also have the knowledge of the
standard deviations of the perturbations. We derive the safe convex
approximations of such chance constrained portfolio problems by using some
suitable generating functions such as a piecewise linear function, an
exponential function, and a piecewise quadratic function. These safe
approximations are the robust counterparts to our ambiguous chance constrained
problem and they are computationally tractable due to the convex nature of
these approximations.
