英文标题：
《Insider Trading with Penalties》
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作者：
Sylvain Carr\\\'e (EPFL), Pierre Collin-Dufresne (EPFL), Franck Gabriel
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最新提交年份：
2018
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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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中文摘要：
我们考虑了Kyle（1985）提出的一个期限框架，在该框架中，内幕人士如果进行交易，可能会受到处罚。当噪声是一致的时，我们建立了几乎任何罚函数平衡点的存在性和唯一性。在均衡状态下，内部人的需求和价格函数通常是非线性的，并且由于预期价格函数是线性的，因此在分析上仍然可以处理。我们利用这一结果来研究价格效率和“公平”之间的权衡：我们考虑一个监管机构，它希望在给定水平的未知情交易者损失情况下，最小化交易后标准差。最小化在惩罚函数空间上；对于每一种可能的惩罚，我们的存在唯一性定理可以明确定义交易后的标准差和均衡中普遍存在的未知情交易者损失。最优惩罚以封闭形式表示。对于小订单，它们必须随着内幕人士订单的数量迅速增加，而对于大订单，它们必须持平：在基本面实现非常高或非常低的价值的情况下，内幕人士发现，尽管罚款很高，但交易是最佳的。虽然这种交易如果发生对流动性交易者来说代价高昂，但它们预示着极端事件，因此会将大量信息纳入价格。我们通过对监管机构施加预算约束并考虑非金钱或金钱处罚的情况，从两个方向概括了这一结果。在第一种情况下，我们确定最优惩罚是先前最优惩罚的子集：均衡贸易量和价格的模式不变。在第二种情况下，我们还充分刻画了约束有效点和惩罚，并表明内幕交易者的需求计划和相关价格函数中出现了新的模式。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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