Robust Mean-Covariance Solutions for Stochastic Optimization

摘要: We provide a method for deriving robust solutions to certain stochastic optimization problems, based on mean-covariance information about the distributions underlying uncertain vector of returns. prove that general class objective functions, amount solving deterministic parametric quadratic program. first projection property multivariate with given means and covariances, which reduces our problem optimizing univariate mean-variance objective. This allows us use known results in multidimensional setting, add new this direction. In particular, we characterize functions (the so-called one- or two-point support functions), is reduced one variable. Finally, adapt result from Geoffrion (1967a) reduce main are true increasing concave utilities convex concave-convex derivatives. Closed-form obtained special discontinuous criteria, motivated by bonus- commission-based incentive schemes portfolio management. also investigate multiproduct pricing application, motivates extensions case nonnegative decision-dependent