MARKOVIAN NASH EQUILIBRIUM IN FINANCIAL MARKETS WITH ASYMMETRIC INFORMATION AND RELATED FORWARD-BACKWARD SYSTEMS

• 成果类型: Article
• 署名作者: Cetin, Umut; Danilova, Albina
• 署名单位: University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1138
• 发表日期: 2016
• 页码: 1996-2029
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; risk-aversion; CONTINUOUS AUCTIONS; quadratic growth; continuous-time; inventories; uniqueness; exchange; BSDEs

摘要

This paper develops a new methodology for studying continuous-time Nash equilibrium in a financial market with asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by the current literature. It turns out that, when the market makers are risk averse, the optimal strategies of the agents are solutions of a forward backward system of partial and stochastic differential equations. In particular, the price set by the market makers solves a nonstandard quadratic backward stochastic differential equation. The main result of the paper is the existence of a Markovian solution to this forward backward system on an arbitrary time interval, which is obtained via a fixed-point argument on the space of absolutely continuous distribution functions. Moreover, the equilibrium obtained in this paper is able to explain several stylized facts which are not captured by the current asymmetric information models.