诚实交易与内幕交易中诚实者的机会
Chances for the honest in honest versus insider trading
摘要：
我们研究了一个有限时间范围内的Black-Scholes市场和两个投资者：一个诚实的和一个内幕交易者。我们用预期随机分析分两步进行分析。首先，我们恢复了经典的投资组合优化的结果，表明预期的对数效用的内部人员是严格大于的诚实的交易者。然后，我们证明了，只要市场是可行的，诚实的交易者可以得到更高的对数效用，因此更多的财富，比内部人严格正概率。我们的证明依赖于分析的Doléans-Dade指数过程的一种前向积分变体。主要的金融结论是，对数效用对一些内部人士来说可能过于保守。
英文摘要：
We study a Black-Scholes market with a finite time horizon and two investors: an honest and an insider trader. We analyze it with anticipating stochastic calculus in two steps. First, we recover the classical result on portfolio optimization that shows that the expected logarithmic utility of the insider is strictly greater than that of the honest trader. Then, we prove that, whenever the market is viable, the honest trader can get a higher logarithmic utility, and therefore more wealth, than the insider with a strictly positive probability. Our proof relies on the analysis of a sort of forward integral variant of the Doléans-Dade exponential process. The main financial conclusion is that the logarithmic utility is perhaps too conservative for some insiders.
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