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.

中文翻译：

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随机期限内有记忆的内幕交易

在本文中，我们研究了一个连续时间内幕交易模型，其中噪声交易者有一些记忆，交易在随机截止日期停止。通过分数布朗运动滤波理论和随机最大值原理，我们得到了内部人最优策略的必要条件，即满足方程。结果表明，当噪声交易者的波动性恒定且噪声交易者的记忆力越来越弱时，最优交易强度和相应的剩余信息分别趋向于噪声交易者没有任何记忆时的情况。并且，数值模拟表明，如果内幕交易的交易强度和噪声交易的波动性都与交易时间无关，内部人的预期利润总是低于在有限固定时间披露资产价值时的预期利润；这是因为未来的交易时间是一个随机截止日期，这会导致内幕信息的丢失。