A market model with medium/long-term effects due to an insider
A market model with medium/long-term effects due to an insider
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DOI：
10.1080/14697688.2012.695084
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发表时间：
2013-03
影响因子：
1.3
通讯作者：
H. Hata;A. Kohatsu-Higa
中科院分区：
文献类型：
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作者：
H. Hata;A. Kohatsu-Higa
在本文中，我们考虑对内幕交易的Karatzas-Pikovsky模型进行修正。具体来说，我们假设内部人通过随机微分方程的漂移影响Black-Scholes型模型的中长期演化。如果满足以下三个条件，我们认为内幕代理人使用的投资组合导致部分均衡：(a)内幕代理人使用的投资组合导致股票价格在他/她自己的过滤下为半鞅，并且他/她自己的过滤随着最终价格的增大而增大；(b)内部人使用的投资组合是最优的，即当他/她的过滤固定时，它使内部人的对数效用最大化；(c) (b)的最优对数效用是有限的。我们给出了部分平衡存在的充分条件，并在一些显式模型中说明了如何应用这些一般结果。
In this article, we consider a modification of the Karatzas–Pikovsky model of insider trading. Specifically, we suppose that the insider agent influences the long/medium-term evolution of Black–Scholes type model through the drift of the stochastic differential equation. We say that the insider agent is using a portfolio leading to a partial equilibrium if the following three properties are satisfied: (a) the portfolio used by the insider leads to a stock price which is a semimartingale under his/her own filtration and his/her own filtration enlarged with the final price; (b) the portfolio used by the insider is optimal in the sense that it maximises the logarithmic utility for the insider when his/her filtration is fixed; and (c) the optimal logarithmic utility in (b) is finite. We give sufficient conditions for the existence of a partial equilibrium and show in some explicit models how to apply these general results.