关键词: 连续内部交易, 风险中性, 相关私有信号, 线性贝叶斯均衡, 市场深度, 剩余信息

Abstract:

A model of continuous-time insider trading in which a risk-neutral insider possesses two imperfect correlated signals of a risky asset is studied. By conditional expectation theory and filtering theory, we first establish three lemmas: normal correlation, equivalent pricing and equivalent profit, which can guarantee to turn our model into a model with insider knowing full information. Then we investigate the impact of the two correlated signals on the market equilibrium consisting of optimal insider trading strategy and semi-strong pricing rule. It shows that in the equilibrium, (1) the market depth is constant over time; (2) if the two noisy signals are not linerly correlated, then all private information of the insider is incorporated into prices in the end while the whole information on the asset value can not incorporated into prices in the end; (3) if the two noisy signals are linear correlated such that the insider can infer the whole information of the asset value, then our model turns into a model with insider knowing full information; (4) if the two noisy signals are the same then the total ex ant profit of the insider is increasing with the noise decreasing, while down to 0 as the noise going up to infinity; (5) if the two noisy signals are not linear correlated then with one noisy signal fixed, the total ex ante profit of the insider is single-peaked with a unique minimum with respect to the other noisy signal value, and furthermore as the noisy value going to 0 it gets its maximum, the profit in the case that the real value is observed.

Key words: continuous-time insider trading, risk neutral, private correlated signals, linear bayesian equilibrium, market depth, residual information