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摘要翻译：
在本文中，我们完成并扩展了我们以前关于随机控制应用于具有库存约束和定向押注的高频做市的工作。如果整个系统是马尔可夫的，我们的新模型允许多个状态变量（如市场价差、随机波动性和市场订单强度）。在零库存风险的情况下，相应的HJB方程的解是精确的。库存风险以两种方式发挥作用：基于波动性的路径依赖惩罚和基于市场价差的到期惩罚。对库存风险参数进行摄动分析，得到了最优解及其一阶控制。我们还包括交易费用；我们发现做市商的价差被扩大以补偿交易成本，但每个交易价差的预期收益保持不变。我们进行了几个数值模拟来评估参数对PNL的影响，特别是显示了定向bet和库存风险如何改变PNL密度的形状。最后，我们将我们的结果推广到多ASET做市策略的情形；我们证明了正确的库存风险概念是（多维）库存相对于库存惩罚的L2范数。
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英文标题：
《High-frequency market-making for multi-dimensional Markov processes》
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作者：
Pietro Fodra, Mauricio Labadie
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最新提交年份：
2013
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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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英文摘要：
In this paper we complete and extend our previous work on stochastic control applied to high frequency market-making with inventory constraints and directional bets. Our new model admits several state variables (e.g. market spread, stochastic volatility and intensities of market orders) provided the full system is Markov. The solution of the corresponding HJB equation is exact in the case of zero inventory risk. The inventory risk enters into play in two ways: a path-dependent penalty based on the volatility and a penalty at expiry based on the market spread. We perform perturbation methods on the inventory risk parameter and obtain explicitly the solution and its controls up to first order. We also include transaction costs; we show that the spread of the market-maker is widened to compensate the transaction costs, but the expected gain per traded spread remains constant. We perform several numerical simulations to assess the effect of the parameters on the PNL, showing in particular how the directional bet and the inventory risk change the shape of the PNL density. Finally, we extend our results to the case of multi-aset market-making strategies; we show that the correct notion of inventory risk is the L2-norm of the (multi-dimensional) inventory with respect to the inventory penalties.
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PDF链接：
https://arxiv.org/pdf/1303.7177
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