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Polyhedral Risk Measures and Lagrangian Relaxation in Electricity Portfolio Optimization

Authors: Andreas Eichhorn, Werner Römisch, and Isabel Wegner

Published in: Dagstuhl Seminar Proceedings, Volume 5031, Algorithms for Optimization with Incomplete Information (2005)

Abstract

We present a multistage stochastic programming model for mean-risk optimization of electricity portfolios containing physical components and energy derivative products. Stochasticity enters the model via the uncertain (time-dependent) prices and electricity demand. The objective is to maximize the expected overall revenue and, simultaneously, to minimize a multiperiod risk measure, i.e., a risk measure that takes into account the intermediate time cash values. We compare the effect of different multiperiod risk measures taken from the class of polyhedral risk measures which was suggested in our earlier work. Furthermore, we discuss how such a mean-risk optimization problem can be solved by dual decomposition techniques (Lagrangian relaxation).

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Andreas Eichhorn, Werner Römisch, and Isabel Wegner. Polyhedral Risk Measures and Lagrangian Relaxation in Electricity Portfolio Optimization. In Algorithms for Optimization with Incomplete Information. Dagstuhl Seminar Proceedings, Volume 5031, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{eichhorn_et_al:DagSemProc.05031.23,
  author =	{Eichhorn, Andreas and R\"{o}misch, Werner and Wegner, Isabel},
  title =	{{Polyhedral Risk Measures and Lagrangian Relaxation in Electricity Portfolio Optimization}},
  booktitle =	{Algorithms for Optimization with Incomplete Information},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5031},
  editor =	{Susanne Albers and Rolf H. M\"{o}hring and Georg Ch. Pflug and R\"{u}diger Schultz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05031.23},
  URN =		{urn:nbn:de:0030-drops-574},
  doi =		{10.4230/DagSemProc.05031.23},
  annote =	{Keywords: Stochastic Programming , Mean-Risk Optimization , Risk Measure , Lagrangian Relaxation , Electricity;}
}

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Polyhedral Risk Measures and Lagrangian Relaxation in Electricity Portfolio Optimization

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