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Moment calculations for piecewise-defined functions: an application to stochastic optimization with coherent risk measures

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  • E. Borgonovo
  • L. Peccati

Abstract

This work introduces a new analytical approach to the formulation of optimization problems with piecewise-defined (PD) objective functions. First, we introduce a new definition of multivariate PD functions and derive formal results for their continuity and differentiability. Then, we obtain closed-form expressions for the calculation of their moments. We apply these findings to three classes of optimization problems involving coherent risk measures. The method enables one to obtain insights on problem structure and on sensitivity to imprecision at the problem formulation stage, eliminating reliance on ad-hoc post-optimality numerical calculations. Copyright Springer Science+Business Media, LLC 2010

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  • E. Borgonovo & L. Peccati, 2010. "Moment calculations for piecewise-defined functions: an application to stochastic optimization with coherent risk measures," Annals of Operations Research, Springer, vol. 176(1), pages 235-258, April.
    • Handle: RePEc:spr:annopr:v:176:y:2010:i:1:p:235-258:10.1007/s10479-008-0504-1
    DOI: 10.1007/s10479-008-0504-1
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    Cited by:

    1. Emanuele Borgonovo & Elmar Plischke & Giovanni Rabitti, 2022. "Interactions and computer experiments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1274-1303, September.
    2. Borgonovo, Emanuele & Tonoli, Fabio, 2014. "Decision-network polynomials and the sensitivity of decision-support models," European Journal of Operational Research, Elsevier, vol. 239(2), pages 490-503.

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