英文标题：
《Optimal market making under partial information with general intensities》
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作者：
Diego Zabaljauregui and Luciano Campi
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最新提交年份：
2020
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英文摘要：
  Starting from the Avellaneda-Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes, but also on unobservable factors modelled by a hidden Markov chain. We tackle this stochastic control problem under partial information with a model that unifies and generalizes many existing ones under full information, combining several risk metrics and constraints, and using general decreasing intensity functionals. We use stochastic filtering, control and piecewise-deterministic Markov processes theory, to reduce the dimensionality of the problem and characterize the reduced value function as the unique continuous viscosity solution of its dynamic programming equation. We then solve the analogous full information problem and compare the results numerically through a concrete example. We show that the optimal full information spreads are biased when the exact market regime is unknown, and the market maker needs to adjust for additional regime uncertainty in terms of P&L sensitivity and observed order flow volatility. This effect becomes higher, the longer the waiting time in between orders.
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中文摘要：
从Avellaneda-Stoikov框架开始，我们考虑一个做市商，她希望在有限的时间范围内最优地设定买卖报价，以最大化其预期效用。她收到的订单的强度不仅取决于她引用的价差，还取决于由隐马尔可夫链建模的不可观察因素。我们用一个模型来解决部分信息下的随机控制问题，该模型在完全信息下统一和推广了许多现有的模型，结合了多个风险度量和约束，并使用一般的递减强度泛函。利用随机滤波、控制和分段确定马尔可夫过程理论，对问题进行降维，并将降维函数刻画为其动态规划方程的唯一连续粘性解。然后，我们解决了类似的全信息问题，并通过一个具体的例子对结果进行了数值比较。我们表明，当准确的市场制度未知时，最优的完全信息利差是有偏差的，做市商需要根据损益敏感性和观察到的订单流波动性调整额外的制度不确定性。这种影响越大，订单之间的等待时间越长。
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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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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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