Radner equilibrium and systems of quadratic BSDEs with discontinuous generators

TL;DR

This paper proves the existence of solutions for a class of quadratic BSDEs with discontinuous generators and applies these results to establish the existence of an incomplete Radner equilibrium in a stochastic endowment economy.

Contribution

It introduces new methods to handle discontinuities in quadratic BSDEs and demonstrates their application in economic equilibrium models.

Findings

Existence of solutions for quadratic BSDEs with discontinuous generators.

Radner equilibrium exists in a stochastic endowment economy with endogenous volatility.

Abstract

Motivated by an equilibrium problem, we establish the existence of a solution for a family of Markovian backward stochastic differential equations with quadratic nonlinearity and discontinuity in $Z$. Using unique continuation and backward uniqueness, we show that the set of discontinuity has measure zero. In a continuous-time stochastic model of an endowment economy, we prove the existence of an incomplete Radner equilibrium with nondegenerate endogenous volatility.