Radner equilibria under ambiguous volatility - Patrick Beißner (Bielefeld University, Center for Mathematical Economics (IMW), 2013)
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: G10; D50; C62; 330; 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