Insider Trading with Memory under Random Deadline
In this paper, we study a model of continuous-time insider trading in which noise traders have some memories and the trading stops at a random deadline. By a filtering theory on fractional Brownian motion and the stochastic maximum principle, we obtain a necessary condition of the insider’s optimal...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2973361 |
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| _version_ | 1832560533549613056 |
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| author | Kai Xiao Yonghui Zhou |
| author_facet | Kai Xiao Yonghui Zhou |
| author_sort | Kai Xiao |
| collection | DOAJ |
| description | In this paper, we study a model of continuous-time insider trading in which noise traders have some memories and the trading stops at a random deadline. By a filtering theory on fractional Brownian motion and the stochastic maximum principle, we obtain a necessary condition of the insider’s optimal strategy, an equation satisfied. It shows that when the volatility of noise traders is constant and the noise traders’ memories become weaker and weaker, the optimal trading intensity and the corresponding residual information tend to those, respectively, when noise traders have no any memory. And, numerical simulation illustrates that if both the trading intensity of the insider and the volatility of noise trades are independent of trading time, the insider’s expected profit is always lower than that when the asset value is disclosed at a finite fixed time; this is because the trading time ahead is a random deadline which yields the loss of the insider’s information. |
| format | Article |
| id | doaj-art-8736c006f7ee4d0ebd56f906dbdec5ab |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-8736c006f7ee4d0ebd56f906dbdec5ab2025-02-03T01:27:22ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/29733612973361Insider Trading with Memory under Random DeadlineKai Xiao0Yonghui Zhou1School of Mathematics, Guizhou Normal University, Guiyang 550001, ChinaSchool of Big Data and Computer Science, Guizhou Normal University, Guiyang 550001, ChinaIn this paper, we study a model of continuous-time insider trading in which noise traders have some memories and the trading stops at a random deadline. By a filtering theory on fractional Brownian motion and the stochastic maximum principle, we obtain a necessary condition of the insider’s optimal strategy, an equation satisfied. It shows that when the volatility of noise traders is constant and the noise traders’ memories become weaker and weaker, the optimal trading intensity and the corresponding residual information tend to those, respectively, when noise traders have no any memory. And, numerical simulation illustrates that if both the trading intensity of the insider and the volatility of noise trades are independent of trading time, the insider’s expected profit is always lower than that when the asset value is disclosed at a finite fixed time; this is because the trading time ahead is a random deadline which yields the loss of the insider’s information.http://dx.doi.org/10.1155/2021/2973361 |
| spellingShingle | Kai Xiao Yonghui Zhou Insider Trading with Memory under Random Deadline Journal of Mathematics |
| title | Insider Trading with Memory under Random Deadline |
| title_full | Insider Trading with Memory under Random Deadline |
| title_fullStr | Insider Trading with Memory under Random Deadline |
| title_full_unstemmed | Insider Trading with Memory under Random Deadline |
| title_short | Insider Trading with Memory under Random Deadline |
| title_sort | insider trading with memory under random deadline |
| url | http://dx.doi.org/10.1155/2021/2973361 |
| work_keys_str_mv | AT kaixiao insidertradingwithmemoryunderrandomdeadline AT yonghuizhou insidertradingwithmemoryunderrandomdeadline |