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Radner equilibrium and systems of quadratic BSDEs with discontinuous generators

Luis Escauriaza, Daniel C. Schwarz and Hao Xing

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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.

Date: 2020-08, Revised 2021-05
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