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Radner Equilibria Under Ambiguous Volatility

48 Pages Posted: 13 Dec 2013  

Patrick Beissner

Bielefeld University - Center for Mathematical Economics

Date Written: December 9, 2013

Abstract

The present paper considers a class of general equilibrium economics when the primitive uncertainty model features uncertainty about continuous-time volatility. This requires a set of mutually singular priors, which do not share the same null sets. For this setting we introduce an appropriate commodity space and the dual of linear and continuous price systems. All agents in the economy are heterogeneous in their preference for uncertainty. Each utility functional is a variational type. The existence of equilibrium is approached by a generalized excess utility fixed point argument. Such Arrow-Debreu allocations can be implemented into a Radner economy with continuous-time trading. Effective completeness of the market spaces alters to an endogenous property. Only mean unambiguous claims equivalently satisfying the classical martingale representation property build the marketed space.

Keywords: Knightian uncertainty, variational preferences, general equilibrium, mutually singular priors, dynamic consistency, volatility uncertainty, excess utility map, gross substitutes, risk adjusted priors, sublinear-expectation, Radner implementation, incomplete markets

JEL Classification: G10, D50, C62

Suggested Citation

Beissner, Patrick, Radner Equilibria Under Ambiguous Volatility (December 9, 2013). Institute of Mathematical Economics Working Paper No. 493. Available at SSRN: https://ssrn.com/abstract=2366360 or http://dx.doi.org/10.2139/ssrn.2366360

Patrick Beissner (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

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