KYLE-BACK MODELS WITH RISK AVERSION AND NON-GAUSSIAN BELIEFS

• 成果类型: Article
• 署名作者: Bose, Shreya; Ekren, Ibrahim
• 署名单位: State University System of Florida; Florida State University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1905
• 发表日期: 2023
• 页码: 4238-4271
• 关键词: Asymmetric information; imperfect competition; CONTINUOUS AUCTIONS; equilibrium; MARKET; transportation; uniqueness; STABILITY

摘要

We show that the problem of existence of equilibrium in Kyle's con-tinuous time insider trading model can be tackled by considering a forward -backward system coupled via an optimal transport type constraint at maturity. The forward component is a stochastic differential equation representing an endogenously determined state variable and the backward component is a quasilinear parabolic equation representing the pricing function. By obtain-ing a stochastic representation for the solution of such a system, we show the well-posedness of solutions and study the properties of the equilibrium ob-tained for small enough risk aversion parameter. In our model, the insider has exponential type utility and the belief of the market maker on the distribution of the price at final time can be non-Gaussian.