英文标题：
《High frequency trading and asymptotics for small risk aversion in a
Markov renewal model》
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作者：
Pietro Fodra, Huy\\^en Pham
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最新提交年份：
2015
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英文摘要：
We study a an optimal high frequency trading problem within a market microstructure model designed to be a good compromise between accuracy and tractability. The stock price is driven by a Markov Renewal Process (MRP), while market orders arrive in the limit order book via a point process correlated with the stock price itself. In this framework, we can reproduce the adverse selection risk, appearing in two different forms: the usual one due to big market orders impacting the stock price and penalizing the agent, and the weak one due to small market orders and reducing the probability of a profitable execution. We solve the market making problem by stochastic control techniques in this semi-Markov model. In the no risk-aversion case, we provide explicit formula for the optimal controls and characterize the value function as a simple linear PDE. In the general case, we derive the optimal controls and the value function in terms of the previous result, and illustrate how the risk aversion influences the trader strategy and her expected gain. Finally, by using a perturbation method, approximate optimal controls for small risk aversions are explicitly computed in terms of two simple PDE\'s, reducing drastically the computational cost and enlightening the financial interpretation of the results.
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中文摘要：
我们在一个市场微观结构模型中研究了一个最优高频交易问题，该模型旨在在准确性和可处理性之间达成良好的折衷。股票价格由马尔可夫更新过程（MRP）驱动，而市场订单通过与股票价格本身相关的点过程到达限价订单簿。在这个框架中，我们可以复制逆向选择风险，它以两种不同的形式出现：通常是由于大的市场订单影响股票价格并惩罚代理人，而较弱的是由于小的市场订单并降低盈利执行的概率。在这个半马尔可夫模型中，我们利用随机控制技术来解决做市问题。在无风险规避的情况下，我们给出了最优控制的显式公式，并将值函数描述为一个简单的线性偏微分方程。在一般情况下，我们根据前面的结果导出了最优控制和价值函数，并说明了风险规避如何影响交易者的策略和预期收益。最后，利用摄动法，用两个简单的偏微分方程显式地计算了小风险规避的近似最优控制，大大降低了计算成本，并启发了对结果的财务解释。
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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：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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