Insider trading with dynamic asset under market makers' partial observations

Jixiu Qiu; Yonghui Zhou; Jixiu Qiu; Yonghui Zhou

doi:10.3934/math.20231277

AIMS Mathematics

2023, Volume 8, Issue 10: 25017-25036. doi: 10.3934/math.20231277

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Research article

Insider trading with dynamic asset under market makers' partial observations

Jixiu Qiu ¹,
Yonghui Zhou ^{2
,
,}

1.
School of Mathematics and Sciences, Guizhou Normal University, Guiyang 550025, China
2.
School of Big Data and Computer Science, Guizhou Normal University, Guiyang 550025, China

Received: 16 June 2023 Revised: 22 July 2023 Accepted: 09 August 2023 Published: 28 August 2023
MSC : 60G35, 60H10, 91G80, 93E11

This paper studies an extended continuous-time insider trading model of Calentey and Stacchetti (2010, Econometrica), which allows market makers to observe some partial information about a dynamic risky asset. For each of the two cases with trading until either a fixed time or a random time, we establish the existence and uniqueness of linear Bayesian equilibrium, consisting of insider trading intensity, price pressure on market orders and price pressure on asset observations. It shows that at each of the two equilibria, all information on the risky asset is incorporated in the market price and when the volatility of observation noise keeps constant, the more information observed by market makers, the smaller price pressure on market orders but the greater price pressure on asset observations such that the insider earns less profit and vice versa. It suggests that the partial observation of market makers weakens the information advantage of the insider, which prevents the insider from monopolizing the market to make excessive profit, then reduces the losses of noise traders, thus improving the fairness and effectiveness in the insider trading market.
- Bayesian equilibrium,
- continuous-time insider trading,
- dynamic programming,
- filtering,
- partial observation
Citation: Jixiu Qiu, Yonghui Zhou. Insider trading with dynamic asset under market makers' partial observations[J]. AIMS Mathematics, 2023, 8(10): 25017-25036. doi: 10.3934/math.20231277

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Abstract

This paper studies an extended continuous-time insider trading model of Calentey and Stacchetti (2010, Econometrica), which allows market makers to observe some partial information about a dynamic risky asset. For each of the two cases with trading until either a fixed time or a random time, we establish the existence and uniqueness of linear Bayesian equilibrium, consisting of insider trading intensity, price pressure on market orders and price pressure on asset observations. It shows that at each of the two equilibria, all information on the risky asset is incorporated in the market price and when the volatility of observation noise keeps constant, the more information observed by market makers, the smaller price pressure on market orders but the greater price pressure on asset observations such that the insider earns less profit and vice versa. It suggests that the partial observation of market makers weakens the information advantage of the insider, which prevents the insider from monopolizing the market to make excessive profit, then reduces the losses of noise traders, thus improving the fairness and effectiveness in the insider trading market.

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