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A new approach to optimizing or hedging a portfolio of financial positions is presented and tested with applications to energy market. Motivated by uncertainty in the estimation of problem data we consider robust bi-objective optimization problems with mean and conditional value-at-risk objective functions where the underlying probability distribution of portfolio return is only known to belong to a certain set. To tackle the problem of uncertainty we consider two different approaches: in the first one, uncertainty is represented by an elliptic set centered at the sample estimators of mean and covariance matrix; in the second one, uncertainty takes into account experts beliefs. For both approaches, we derive analytical semi-closed-form solutions for the worst case mean-CVaR portfolio; in addition, we provide a characterization of the location of the robust Pareto frontier with respect to the corresponding original Pareto frontier. • Exploration of the robust mean-CVaR optimal portfolios through bi-objective programming. • Derivation of the analytical expressions based on commonly assumed ambiguity sets. • Comparison of the robust frontiers to the nominal mean-CVaR Pareto frontier. • Construction of a model where investors consider recommendations from multiple experts regarding input parameters without imposing any distributional assumptions on portfolio returns. • Analysis of how changes in the risk aversion parameter, linked to the scalarized optimization problem, affect optimal portfolio compositions. • Practical application of the robust bi-objective optimization in stock markets.
Hitaj et al. (Sat,) studied this question.