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SPEPS Preprint

Author(s): Morten Riis, University of Aarhus
Rüdiger Schultz, Gerhard-Mercator University Duisburg
Title: Applying the minimum risk criterion in stochastic recourse programs
Date of Acceptance: 26.06.2001
Submission Date: 20.04.2001
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Appeared in: Computational optimization and applications : an international journal 2-3 (Vol. 24, 2003)
Springer Science + Business Media B.V. (New York, NY [u.a.])
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Abstract (eng):
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 or 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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