摘要翻译：
本论文所讨论的主题具有内在的双重性。第一部分考虑做市商在有限的时间范围内最优设置出价/出价的问题，以使其期望效用最大化。她收到的订单的强度不仅取决于她所引用的价差，还取决于由隐马尔可夫链建模的不可观察的因素。利用随机滤波、控制和PDMPs理论解决了部分信息下的随机控制问题。该值函数被刻画为其动态规划方程的唯一连续粘性解，并与它的全信息对应体进行了数值比较。当准确的市场机制未知时，最优全信息价差是有偏差的，因为做市商需要根据PnL敏感性和可观察到的订单流波动性来调整额外的机制不确定性。第二部分讨论非零和随机脉冲控制对策的数值求解。这些问题提供了一个现实和深远的模型框架，但解决这些问题的困难阻碍了它们的扩散。提出了一种策略迭代型求解器来求解拟变分不等式组，并用数值方法对其进行了验证，得到了令人满意的结果。最后，重点研究了具有对称结构的博弈，并提出了一种改进算法。在对角占优矩阵弱链的情况下，对博弈者的策略进行了严格的收敛性分析，并对博弈者的策略进行了自然假设，从而得到了图论的解释。该算法用于计算具有挑战性的问题的高精度均衡收益和纳什均衡，甚至一些结果超出了现有理论的范围。
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英文标题：
《Optimal market making under partial information and numerical methods
  for impulse control games with applications》
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作者：
Diego Zabaljauregui
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最新提交年份：
2020
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分类信息：

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：Computer Science        计算机科学
二级分类：Numerical Analysis        数值分析
分类描述：cs.NA is an alias for math.NA. Roughly includes material in ACM Subject Class G.1.
cs.na是Math.na的别名。大致包括ACM学科类G.1的材料。
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一级分类：Economics        经济学
二级分类：General Economics        一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Mathematics        数学
二级分类：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Quantitative Finance        数量金融学
二级分类：Economics        经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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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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英文摘要：
  The topics treated in this thesis are inherently two-fold. The first part considers the problem of a market maker optimally setting 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. This stochastic control problem under partial information is solved by means of stochastic filtering, control and PDMPs theory. The value function is characterized as the unique continuous viscosity solution of its dynamic programming equation and numerically compared with its full information counterpart. The optimal full information spreads are shown to be biased when the exact market regime is unknown, as the market maker needs to adjust for additional regime uncertainty in terms of PnL sensitivity and observable order flow volatility.   The second part deals with numerically solving nonzero-sum stochastic impulse control games. These offer a realistic and far-reaching modelling framework, but the difficulty in solving such problems has hindered their proliferation. A policy-iteration-type solver is proposed to solve an underlying system of quasi-variational inequalities, and it is validated numerically with reassuring results.   Eventually, the focus is put on games with a symmetric structure and an improved algorithm is put forward. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. The algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise too challenging problems, and even some for which results go beyond the scope of the currently available theory.
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PDF链接：
https://arxiv.org/pdf/2009.06521