内幕交易与处罚
Insider Trading with Penalties
摘要：
我们考虑一个单期Kyle（1985）框架，如果内部人交易，她可能会受到惩罚。当噪声是均匀的时，我们建立了几乎任何罚函数平衡的存在性和唯一性。在均衡中，内部人的需求和价格函数一般都是非线性的，并且由于预期价格函数是线性的，所以在分析上仍然是可处理的。我们使用这个结果来研究价格效率和“公平性”之间的权衡：我们考虑一个监管机构，希望最小化交易后的标准差为一个给定的水平不知情的交易者的损失。最小化是在处罚的函数空间上进行的;对于每种可能的处罚，我们的存在性和唯一性定理允许明确定义均衡中普遍存在的交易后标准差和不知情交易者的损失。最优处罚以封闭形式表征。对于小额订单，它们必须随着内部人订单的大小迅速增加，而对于大额订单，它们必须变得平坦：在基本面以非常高或非常低的价值实现的情况下，内部人发现尽管罚款很高，但交易是最佳的。尽管这种交易（如果发生的话）对流动性交易者来说代价高昂，但它们预示着极端事件，因此将大量信息纳入价格。我们概括了这一结果在两个方向施加预算约束的监管机构，并考虑无论是非金钱或金钱处罚的情况下。在第一种情况下，我们建立了最优惩罚是以前的最优惩罚的子集：均衡交易量和价格的模式是不变的。在第二种情况下，我们还充分表征了约束有效点和处罚，并表明新的模式出现在需求时间表的内幕交易者和相关的价格函数。
英文摘要：
We consider a one-period Kyle (1985) framework where the insider can be subject to a penalty if she trades. We establish existence and uniqueness of equilibrium for virtually any penalty function when noise is uniform. In equilibrium, the demand of the insider and the price functions are in general non-linear and remain analytically tractable because the expected price function is linear. We use this result to investigate the trade off between price efficiency and 'fairness': we consider a regulator that wants to minimise post-trade standard deviation for a given level of uninformed traders' losses. The minimisation is over the function space of penalties; for each possible penalty, our existence and uniqueness theorem allows to define unambiguously the post-trade standard deviation and the uninformed traders' losses that prevail in equilibrium.Optimal penalties are characterized in closed-form. They must increase quickly with the magnitude of the insider's order for small orders and become flat for large orders: in cases where the fundamental realizes at very high or very low values, the insider finds it optimal to trade despite the high penalty. Although such trades-if they occur-are costly for liquidity traders, they signal extreme events and therefore incorporate a lot of information into prices. We generalize this result in two directions by imposing a budget constraint on the regulator and considering the cases of either non-pecuniary or pecuniary penalties. In the first case, we establish that optimal penalties are a subset of the previously optimal penalties: the patterns of equilibrium trade volumes and prices is unchanged. In the second case, we also fully characterize the constrained efficient points and penalties and show that new patterns emerge in the demand schedules of the insider trader and the associated price functions.
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