A system of quadratic BSDEs arising in a price impact model
A system of quadratic BSDEs arising in a price impact model
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DOI：
10.1214/15-aap1103
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发表时间：
2014-08
期刊：
影响因子：
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通讯作者：
D. Kramkov;Sergio Pulido
中科院分区：
文献类型：
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作者：
D. Kramkov;Sergio Pulido
我们考虑一个金融模型，其中风险资产的价格由一个考虑外生需求的代表性做市商报价。我们的特点是这些价格的一个系统的二次增长的BSDES。我们证明了这个系统承认一个唯一的解决方案，每一个有界的需求，当且仅当做市商的风险厌恶是足够小的。唯一性是建立在自然类的解决方案，没有任何额外的范数限制。据我们所知，这是第一个研究证明这样的（全球）唯一性结果的完全耦合二次BSDES系统。
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.