RADNER EQUILIBRIUM AND SYSTEMS OF QUADRATIC BSDES WITH DISCONTINUOUS GENERATORS

• 成果类型: Article
• 署名作者: Escauriaza, Luis; Schwarz, Daniel C.; Xing, Hao
• 署名单位: University of Basque Country; University of London; University College London; Boston University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1765
• 发表日期: 2022
• 页码: 3492-3536
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; unique continuation theorem; backward uniqueness; continuous-time; carleman inequalities; parabolic operators; incomplete markets; securities markets; EXISTENCE; landis

摘要

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.