Newsvendor solutions via conditional value-at-risk minimization.

*(English)*Zbl 1275.90057Summary: We consider the minimization of the conditional value-at-risk (CVaR), a most preferable risk measure in financial risk management, in the context of the well-known single-period newsvendor problem, which is originally formulated as the maximization of the expected profit or the minimization of the expected cost. We show that downside risk measures including the CVaR are tractable in the problem due to their convexity, and consequently, under mild assumptions on the probability distribution of products’ demand, we provide analytical solutions or linear programming (LP) formulation of the minimization of the CVaR measures defined with two different loss functions. Numerical examples are also exhibited, clarifying the difference among the models analyzed in this paper, and demonstrating the efficiency of the LP solutions.

##### MSC:

90C25 | Convex programming |

91B30 | Risk theory, insurance (MSC2010) |

##### Keywords:

risk management; newsvendor problem; Conditional Value-at-Risk (CVaR); mean-risk model; convex optimization
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\textit{J.-Y. Gotoh} and \textit{Y. Takano}, Eur. J. Oper. Res. 179, No. 1, 80--96 (2007; Zbl 1275.90057)

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