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Equilibrium Price and Optimal Insider Trading Strategy Under Stochastic Liquidity with Long Memory

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Abstract

In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy, price impact and price volatility are obtained explicitly. The volatility of the price volatility appears excessive, which is a result of the fact that a more aggressive trading strategy is chosen by the insider when uninformed volume is higher. The optimal trading strategy turns out to possess the property of long memory, and the price impact is also affected by the fractional noise.

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Notes

  1. An alternative derivation is to use the standard Gaussian projection theorem [26, Theorems 12.6 and 12.7], as shown in [12].

  2. Similar results have also been reported by other authors, and we would like to readers to refer to the literature, such as [12, Lemma 8] and [13, Sect. 3].

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Acknowledgements

The authors would like to express deep gratitude to the reviewer and the editor for their very helpful suggestions and comments, which have helped us to substantially improve the presentation and quality of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Ben-Zhang Yang & Nan-Jing Huang

  2. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia

    Xin-Jiang He

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  1. Ben-Zhang Yang
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Correspondence to Nan-Jing Huang.

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This work was supported by the National Natural Science Foundation of China (11471230, 11671282).

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Yang, BZ., He, XJ. & Huang, NJ. Equilibrium Price and Optimal Insider Trading Strategy Under Stochastic Liquidity with Long Memory. Appl Math Optim 84, 1209–1237 (2021). https://doi.org/10.1007/s00245-020-09675-2

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