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Dynamic Risked Equilibrium

Author

Listed:
  • Michael Ferris

    (Computer Sciences Department and Wisconsin Institute for Discovery, University of Wisconsin, Madison, Wisconsin 53706)

  • Andy Philpott

    (Electric Power Optimization Centre, Department of Engineering Science, University of Auckland, Auckland 1042, New Zealand)

Abstract

We study a competitive partial equilibrium in markets where risk-averse agents solve multistage stochastic optimization problems formulated in scenario trees. The agents trade a commodity that is produced from an uncertain supply of resources. Both resources and the commodity can be stored for later consumption. Several examples of a multistage risked equilibrium are outlined, including aspects of battery and hydroelectric storage in electricity markets, distributed ownership of competing technologies relying on shared resources, and aspects of water control and pricing. The agents are assumed to have nested coherent risk measures based on one-step risk measures with polyhedral risk sets that have a nonempty intersection over agents. Agents can trade risk in a complete market of Arrow-Debreu securities. In this setting, we define a risk-trading competitive market equilibrium and establish two welfare theorems. Competitive equilibrium will yield a social optimum (with a suitably defined social risk measure) when agents have strictly monotone one-step risk measures. Conversely, a social optimum with an appropriately chosen risk measure will yield a risk-trading competitive market equilibrium when all agents have strictly monotone risk measures. The paper also demonstrates versions of these theorems when risk measures are not strictly monotone.

Suggested Citation

  • Michael Ferris & Andy Philpott, 2022. "Dynamic Risked Equilibrium," Operations Research, INFORMS, vol. 70(3), pages 1933-1952, May.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:3:p:1933-1952
    DOI: 10.1287/opre.2019.1958
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    Citations

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    Cited by:

    1. Abada, Ibrahim & Belkhouja, Mustapha & Ehrenmann, Andreas, 2025. "On the valuation of legacy power production in liberalized markets via option-pricing," European Journal of Operational Research, Elsevier, vol. 322(3), pages 1005-1024.
    2. Abada, I. & Ehrenmann, A., 2025. "Mitigating Market Incompleteness with Minor Market Distortions: The Case of Negative Spot Prices For Electricity," Cambridge Working Papers in Economics 2525, Faculty of Economics, University of Cambridge.
    3. Ibrahim Abada & Andreas Ehrenmann, 2025. "Mitigating market incompleteness with minor market distortions: the case of negative spot prices for electricity," Working Papers EPRG2507, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    4. Shu, Han & Mays, Jacob, 2025. "Transmission benefits and cost allocation under ambiguity," Energy Economics, Elsevier, vol. 141(C).
    5. Feng Runhuan & Liang Zongxia & Song Yilun, 2025. "Decentralized Annuity: A Quest for the Holy Grail of Lifetime Financial Security," Papers 2502.13742, arXiv.org.

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