Robust Portfolio Optimization under Ambiguous Chance Constraints

Abstract: 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.