A market model with medium/long-term effects due to an insider |
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Authors: | Hiroaki Hata |
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Institution: | Graduate School of Engineering Sciences , Osaka University , 1-3 Machikaneyama-cho, Toyonaka 560-8531 , Osaka , Japan |
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Abstract: | 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. |
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Keywords: | Agent based modelling Insider trading Liquidity modelling Market microstructure Mathematical finance Portfolio analysis Stochastic differential equations |
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