Dynamic Risked Equilibrium

Michael Ferris () and Andy Philpott ()
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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

Operations Research, 2022, vol. 70, issue 3, 1933-1952

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.

Keywords: Optimization; coherent risk measure; partial equilibrium; perfect competition; welfare theorem (search for similar items in EconPapers)
Date: 2022
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