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.
Funding Statement
L. Escauriaza is supported by the Basque Government grant IT1247-19 and MICINN grant PGC2018-094522-B-I00.
Acknowledgement
We are grateful to Johannes Muhle-Karbe for helpful comments on the paper.
Citation
Luis Escauriaza. Daniel C. Schwarz. Hao Xing. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators." Ann. Appl. Probab. 32 (5) 3492 - 3536, October 2022. https://doi.org/10.1214/21-AAP1765
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