Dynamic asset risk-seeking insider trading under signal observation

Kai Xiao; Kai Xiao

doi:10.3934/math.2025500

AIMS Mathematics

2025, Volume 10, Issue 5: 11036-11051. doi: 10.3934/math.2025500

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Dynamic asset risk-seeking insider trading under signal observation

Kai Xiao ^,

School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550001, China

Received: 15 February 2025 Revised: 22 April 2025 Accepted: 08 May 2025 Published: 15 May 2025
MSC : 93E11, 93E20

In this paper, we investigated a continuous version of an insider trading model. There were three basic assumptions in this model: (1) the insider exhibited risk-seeking, (2) market makers could receive partial signals regarding the risky asset, and (3) the risky asset was driven by a standard Brownian motion. By employing optimal filtering theory and stochastic control theory, we derived some necessary conditions for market equilibrium. Additionally, we established both the existence and uniqueness of the market equilibrium. At equilibrium, we observed that as time progresses, the insider's residual information gradually diminished when the volatility of the risky asset was low. In contrast, if the volatility was high, the insider's residual information initially increased. Meanwhile, the partial observation coefficient remained constant, while both trading intensity and market liquidity increased over time.
- dynamic asset,
- risk-seeking,
- signal observation,
- HJB equation,
- optimal filtering
Citation: Kai Xiao. Dynamic asset risk-seeking insider trading under signal observation[J]. AIMS Mathematics, 2025, 10(5): 11036-11051. doi: 10.3934/math.2025500

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Abstract

In this paper, we investigated a continuous version of an insider trading model. There were three basic assumptions in this model: (1) the insider exhibited risk-seeking, (2) market makers could receive partial signals regarding the risky asset, and (3) the risky asset was driven by a standard Brownian motion. By employing optimal filtering theory and stochastic control theory, we derived some necessary conditions for market equilibrium. Additionally, we established both the existence and uniqueness of the market equilibrium. At equilibrium, we observed that as time progresses, the insider's residual information gradually diminished when the volatility of the risky asset was low. In contrast, if the volatility was high, the insider's residual information initially increased. Meanwhile, the partial observation coefficient remained constant, while both trading intensity and market liquidity increased over time.

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