Mathematical Finance and Stochastics Seminar by Jianfeng Zhang: Some New Perspectives on Kyle-Back Insider Trading Problems
Speaker: , professor of mathematics, University of Southern California
Title: Some New Perspectives on Kyle-Back Insider Trading Problems
Abstract: A Kyle-Back model consists of three types of agents trading on an asset: 1) a (large) population of noise traders, who are non-strategic and are liquidity providers; 2) an insider, who observes the inside information and invests strategically to maximize his gain; and 3) a market maker, who observes the total order of the insider and the noise traders and sets the market price. This is a Nash game problem between the insider and the market maker. While there are extensive studies in the math finance literature, the existing approaches have some undesirable features, which we aim to overcome.
First, the majority of the existing literature take the PDE approach, which requires certain Markovian structure of the candidate equilibrium. This constraint makes the existence hard, and on the other hand excludes the uniqueness result among possibly non-Markovian equilibria. We shall reformulate the problem as a stochastic differential game and use the FBSDE approach. Under certain technical conditions, we show that the game has a unique equilibrium. This is the first uniqueness result in the literature. Moreover, our equilibrium is not Markovian in the above sense, and thus is beyond the reach of the standard approach in the literature.
Next, in the existing results the insider’s equilibrium strategy has the same scale as the total order of all noise traders. Note that in many applications, the number of noise traders is large, then this scale issue is against the intuition, and more importantly against the medium-sized trades observed in the empirical studies. We shall introduce a model with legal risk and carry out the asymptotic analysis when the number of noise traders goes to infinity. We derive a stealth index for the insider’s trading volume which confirms the medium-sized trades, and show that the limit equilibrium, which is a lot easier to analyze, is an approximate equilibrium for the original problem.
The talk is based on two works, one joint with Bixing Qiao and the other one with Jin Ma and Weixuan Xia.
Stochastic Analysis