Brownian equilibria under Knightian uncertainty
type: Item
instance of: scholarly article
title: Brownian equilibria under Knightian uncertainty
zbMATH Open document ID: 1320.91104
published in: Mathematics and Financial Economics
publication date: 2015-03-24T00:00:00Z
review text: The paper develops the modeling of dynamic stochastic general equilibrium with respect to generalization of agents' utilities representation. The target is being obtained under simplification of general equilibrium to exchange equilibrium, and with preference representation via a stochastic differential formulation of intertemporal recursive utility. The economy consists of \(m \in \mathbb N\) agents with utilities described by the following backward SDEs: \[ dU_t^i=-f^i(t,c_t,U_t^i,\sigma_t^i)dt + {\sigma_t^i}^TdB_t, \; U_T^i=0,\quad i\in \{1,\dots,m\}. \] Here, \(c_t\) is the time-realization of a stochastic consumption process, \(\sigma_t^i\) is the volatility of \(U_t^i\), \(f^i\) is an aggregator function, and \((B_t)\) is an \(n\)-dimensional Brownian motion. The initial value \(U_0^i = E[\int_0^Tf^i(t,c_t,U_t^i,\sigma_t^i)dt]\) is a utility functional of the \(i\)th agent named `generalized stochastic differential utility' (GSDU). Each agent has an endowment \(e^i\). Exchange is defined by utilities \(\{U^i\}\), endowments \(\{e^i\}\) and a price system \(\Pi\) (a linear functional on the commodity space). The equilibrium is defined in these terms as usual in the Arrow-Debreu setting. The main result of the paper is the existence theorem of an equilibrium \((\bar{c}_1,\dots,\bar{c}_m; \Pi)\). The setting generalizes the models of \textit{Z. Chen} and \textit{L. Epstein} [Econometrica 70, No. 4, 1403--1443 (2002; Zbl 1121.91359)] as well as \textit{T. F. Bewley} [Decis. Econ. Finance 25, No. 2, 79--110 (2002; Zbl 1041.91023)] with Knightian uncertainty.
Mathematics Subject Classification ID: 91B51
Mathematics Subject Classification ID: 91B50
Mathematics Subject Classification ID: 91B08
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 6419178
zbMATH Keywords: stochastic differential utility
zbMATH Keywords: intertemporal recursive utility
zbMATH Keywords: Knightian uncertainty
zbMATH Keywords: equilibrium existence
zbMATH Keywords: generic existence
author: Patrick Beissner
reviewed by: Vladimir Gorbunov
MaRDI profile type: Publication
full work available at URL: s11579-014-0133-1
OpenAlex ID: W3125698146
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DOI: 10.1007/S11579-014-0133-1
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description: scientific article; zbMATH DE number 6419178