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Dynamic Risked Equilibrium

Michael Ferris(ferris***at***cs.wisc.edu)
Andy Philpott(a.philpott***at***auckland.ac.nz)

Abstract: We revisit the correspondence of competitive partial equilibrium with a social optimum 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 which can be stored. The agents can also trade risk using Arrow-Debreu securities. In this setting we define a risk-trading 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 Arrow-Debreu 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 risk-trading competitive market equilibrium when all agents have nested strictly monotone coherent risk measures with intersecting polyhedral risk sets, and there are enough Arrow-Debreu 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
Entry Accepted: 04/16/2018
Entry Last Modified: 04/15/2018

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