Linear Bayesian equilibrium in insider trading with a random time under partial observations

Abstract

<abstract><p>In this paper, the insider trading model of Xiao and Zhou (<italic>Acta Mathematicae Applicatae, 2021</italic>) is further studied, in which market makers receive partial information about a static risky asset and an insider stops trading at a random time. With the help of dynamic programming principle, we obtain a unique linear Bayesian equilibrium consisting of insider's trading intensity and market liquidity parameter, instead of none Bayesian equilibrium as before. It shows that (i) as time goes by, both trading intensity and market depth increase exponentially, while residual information decreases exponentially; (ii) with average trading time increasing, trading intensity decrease, but both residual information and insider's expected profit increase, while market depth is a unimodal function with a unique minimum with respect to average trading time; (iii) the less information observed by market makers, the weaker trading intensity and market depth are, but the more both expect profit and residual information are, which is in accord with our economic intuition.</p></abstract>