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

Kai Xiao; Yonghui Zhou; Kai Xiao; Yonghui Zhou

doi:10.3934/math.2021772

AIMS Mathematics

2021, Volume 6, Issue 12: 13347-13357. doi: 10.3934/math.2021772

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Research article

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

Kai Xiao ¹,
Yonghui Zhou ^{2
,
,}

1.
School of Mathematical Sciences, Guizhou Normal University, Guiyang 550001, China
2.
School of Big Data and Computer Science, Guizhou Normal University, Guiyang 550001, China

Received: 03 June 2021 Accepted: 08 September 2021 Published: 16 September 2021
MSC : 93E11, 93E20

In this paper, the insider trading model of Xiao and Zhou (Acta Mathematicae Applicatae, 2021) 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.
- insider trading,
- Bayesian equilibrium,
- random time,
- partial observation,
- HJB equation
Citation: Kai Xiao, Yonghui Zhou. Linear Bayesian equilibrium in insider trading with a random time under partial observations[J]. AIMS Mathematics, 2021, 6(12): 13347-13357. doi: 10.3934/math.2021772

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Abstract

In this paper, the insider trading model of Xiao and Zhou (Acta Mathematicae Applicatae, 2021) 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.

References

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