Dynamic Risked Equilibrium

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 froman 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 riskmeasures based on one-step riskmeasureswith polyhedral risk sets that have a nonempty intersection over agents. Agents can trade risk in a completemarket ofArrow-Debreu securities. In this setting,we define a risk-trading competitivemarket equilibriumand establish twowelfare theorems. Competitive equilibriumwill yield a social optimum(with a suitably defined social risk measure)when agents have strictlymonotone one-step riskmeasures. Conversely, a social optimumwith an appropriately chosen riskmeasurewill yield a risk-trading competitivemarket equilibrium when all agents have strictly monotone risk measures. The paper also demonstrates versions of these theoremswhen riskmeasures are not strictlymonotone. Copyright © 2022 Informs.