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This paper studies Conditional Value-at-Risk (CVaR) with multiple losses. We introduce the concept of α-CVaR for the case of multiple losses under the confidence level vector α. The α-CVaR indicates the conditional expected losses corresponding to the α-VaR. The problem of solving the minimal α-CVaR results in a multiobjective problem (MCVaR). In order to get Pareto efficient solutions of the (MCVaR), we introduce a single objective problem (SCVaR) and show that the optimal solutions of the (SCVaR) are the Pareto efficient solutions of (MCVaR).

A Method on Solving Multiobjective Conditional Value-at-Risk