英文标题：
《Dark-Pool Perspective of Optimal Market Making》
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作者：
M. Alessandra Crisafi, Andrea Macrina
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最新提交年份：
2015
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英文摘要：
  We consider a finite-horizon market-making problem faced by a dark pool that executes incoming buy and sell orders. The arrival flow of such orders is assumed to be random and, for each transaction, the dark pool earns a per-share commission no greater than the half bid-ask spread. Throughout the entire period, the main concern is inventory risk, which increases as the number of held positions becomes critically small or large. The dark pool can control its inventory by choosing the size of the commission for each transaction, so to encourage, e.g., buy orders instead of sell orders. Furthermore, it can submit lit-pool limit orders, of which execution is uncertain, and market orders, which are expensive. In either case, the dark pool risks an information leakage, which we model via a fixed penalty for trading in the lit pool. We solve a double-obstacle impulse-control problem associated with the optimal management of the inventory, and we show that the value function is the unique viscosity solution of the associated system of quasi variational inequalities. We explore various numerical examples of the proposed model, including one that admits a semi-explicit solution.
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中文摘要：
我们考虑了一个有限期做市商问题，该问题由执行传入买卖订单的暗池所面临。假设此类订单的到达流是随机的，对于每笔交易，暗池赚取的每股佣金不超过买卖差价的一半。在整个期间，主要关注的是库存风险，随着持有头寸的数量变得非常小或非常大，库存风险会增加。暗池可以通过选择每笔交易的佣金大小来控制其库存，以鼓励（例如）购买订单而不是销售订单。此外，它还可以提交执行不确定的lit池限额订单和价格昂贵的市场订单。在这两种情况下，暗池都有信息泄露的风险，我们通过对亮池交易的固定惩罚来模拟这种风险。我们解决了一个与库存最优管理相关的双障碍脉冲控制问题，并证明了价值函数是相关拟变分不等式组的唯一粘性解。我们探讨了所提出模型的各种数值例子，包括一个允许半显式解的例子。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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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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