Risk-seeking insider trading with partial observation in continuous time

Kai Xiao; Kai Xiao

doi:10.3934/math.20231440

AIMS Mathematics

2023, Volume 8, Issue 11: 28143-28152. doi: 10.3934/math.20231440

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Risk-seeking insider trading with partial observation in continuous time

Kai Xiao ^,

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

Received: 13 August 2023 Revised: 18 September 2023 Accepted: 25 September 2023 Published: 13 October 2023
MSC : 93E11, 93E20

In this paper, a continuous-time insider trading model is investigated in which an insider is risk-seeking and market makers may receive partial information on the value of a risky asset. With the help of filtering theory and dynamic programming principle, the uniqueness and existence of linear equilibrium is established. It shows that (ⅰ) as time goes by, the residual information decreases, but both the trading intensity and the market liquidity increases, and (ⅱ) with the partial observation accuracy decreasing, both the market liquidity and the residual information will increase while the trading intensity decreases. On the whole, the risk-seeking insider is eager to trade all the trading period, and for market development, it is necessary to increase the insider's risk-preference behavior appropriately.
- insider trading,
- risk-seeking,
- partial observation,
- $ HJB $,
- linear Bayesian equilibrium
Citation: Kai Xiao. Risk-seeking insider trading with partial observation in continuous time[J]. AIMS Mathematics, 2023, 8(11): 28143-28152. doi: 10.3934/math.20231440

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Abstract

In this paper, a continuous-time insider trading model is investigated in which an insider is risk-seeking and market makers may receive partial information on the value of a risky asset. With the help of filtering theory and dynamic programming principle, the uniqueness and existence of linear equilibrium is established. It shows that (ⅰ) as time goes by, the residual information decreases, but both the trading intensity and the market liquidity increases, and (ⅱ) with the partial observation accuracy decreasing, both the market liquidity and the residual information will increase while the trading intensity decreases. On the whole, the risk-seeking insider is eager to trade all the trading period, and for market development, it is necessary to increase the insider's risk-preference behavior appropriately.

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