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Applying the Minimum Risk Criterion in Stochastic Recourse Programs

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Abstract

In the setting of stochastic recourse programs, we consider the problem of minimizing the probability of total costs exceeding a certain threshold value. The problem is referred to as the minimum risk problem and is posed in order to obtain a more adequate description of risk aversion than that of the accustomed expected value problem. We establish continuity properties of the recourse function as a function of the first-stage decision, as well as of the underlying probability distribution of random parameters. This leads to stability results for the optimal solution of the minimum risk problem when the underlying probability distribution is subjected to perturbations. Furthermore, an algorithm for the minimum risk problem is elaborated and we present results of some preliminary computational experiments.

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Authors and Affiliations

  1. Department of Operations Research, University of Aarhus, Building 530, Ny Munkegade, DK—8000, Århus C, Denmark

    Morten Riis

  2. Institute of Mathematics, Gerhard-Mercator University Duisburg, Lotharstraße 65, D—47048, Duisburg, Germany

    Rüdiger Schultz

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  1. Morten Riis
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  2. Rüdiger Schultz
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Correspondence to Morten Riis.

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Riis, M., Schultz, R. Applying the Minimum Risk Criterion in Stochastic Recourse Programs. Computational Optimization and Applications 24, 267–287 (2003). https://doi.org/10.1023/A:1021862109131

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