A SYSTEM OF QUADRATIC BSDES ARISING IN A PRICE IMPACT MODEL

• 成果类型: Article
• 署名作者: Kramkov, Dmitry; Pulido, Sergio
• 署名单位: Carnegie Mellon University; Universite Paris Saclay; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1103
• 发表日期: 2016
• 页码: 794-817
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; incomplete markets; GROWTH

摘要

We consider a financial model where the prices of risky assets are quoted by a representative market maker who takes into account an exogenous demand. We characterize these prices in terms of a system of BSDEs with quadratic growth. We show that this system admits a unique solution for every bounded demand if and only if the market maker's risk-aversion is sufficiently small. The uniqueness is established in the natural class of solutions, without any additional norm restrictions. To the best of our knowledge, this is the first study that proves such (global) uniqueness result for a system of fully coupled quadratic BSDEs.