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Robust mean-covariance solutions for stochastic optimization

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The author provides a method for deriving robust solutions to stochastic optimization problems with general objective, based on mean-covariance information about the distributions underlying the uncertain vector of returns. She proves that for a general class of objective functions, the robust solutions amount to solving a certain deterministic parametric quadratic program. Her approach relies on two key results. First, she proves a general projection property for sets of distributions with given means and covariances, which reduces the problem to a deterministic bi-criteria optimization problem. Second, she adapts a result from Geoffrion (1966) to reduce this problem to solving a parametric quadratic program. In particular the author provides closed form solutions for special quantile-based criteria, such as probability and option-like objectives, value at risk and conditional value at risk. She investigates applications of her results in financial portfolio management, generalized regression and multi-product pricing. Finally, she investigates an extension of these results for the case of non-negative returns.

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