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Michael Ferris(ferriscs.wisc.edu) Abstract: We revisit the correspondence of competitive partial equilibrium with a social optimum in markets where riskaverse agents solve multistage stochastic optimization problems formulated in scenario trees. The agents trade a commodity that is produced from an uncertain supply of resources which can be stored. The agents can also trade risk using ArrowDebreu securities. In this setting we define a risktrading competitive market equilibrium and prove a welfare theorem: competitive equilibrium will yield a social optimum (with a suitably defined social risk measure) when agents have nested coherent risk measures with intersecting polyhedral risk sets, and there are enough ArrowDebreu securities to hedge the uncertainty in resource supply. We also give a proof of the converse result: a social optimum with an appropriately chosen risk measure will yield a risktrading competitive market equilibrium when all agents have nested strictly monotone coherent risk measures with intersecting polyhedral risk sets, and there are enough ArrowDebreu securities to hedge the uncertainty in resource supply. Keywords: coherent risk measure, partial equilibrium, perfect competition, welfare theorem Category 1: Stochastic Programming Category 2: Other Topics (Game Theory ) Citation: Technical Report, Electric Power Optimization Centre, University of Auckland. Download: [PDF] Entry Submitted: 04/15/2018 Modify/Update this entry  
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