英文标题：
《Theoretical and Numerical Analysis of an Optimal Execution Problem with
Uncertain Market Impact》
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作者：
Kensuke Ishitani and Takashi Kato
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最新提交年份：
2015
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英文摘要：
This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.
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中文摘要：
本文是Ishitani和Kato（2015）的延续，在这篇文章中，我们推导出了一个连续时间价值函数，对应于一个最优执行问题，该问题具有不确定的市场影响，作为离散时间价值函数的极限。这里，我们研究了派生值函数的一些性质。特别地，我们证明了该函数是连续的，并且具有半群性质，这与Hamilton-Jacobi-Bellman拟变分不等式密切相关。此外，我们还表明，市场影响中的噪声会导致风险中性评估低估影响成本。我们还研究了伽马分布噪声对数线性/二次市场影响函数下的典型例子。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：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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