摘要翻译:
研究了考虑市场影响的连续时间市场模型中的最优执行问题。我们将该问题化为一个随机控制问题,并研究了相应的值函数的性质。我们发现,对于大销售额,时间起点上的右连续性与市场冲击的强度有关,否则价值函数是连续的。此外,我们给出了半群性质(Bellman原理),并将值函数刻画为相应的Hamilton-Jacobi-Bellman方程的粘性解。本文给出了在具有非线性市场影响的Black-Scholes型市场中,即使交易者是风险中性的情况下,最优策略的形式完全随交易者的证券持有量而改变,最优策略的形式也不是整体平仓而是逐步平仓的例子。
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英文标题:
《An Optimal Execution Problem with Market Impact》
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作者:
Takashi Kato
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最新提交年份:
2014
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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: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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英文摘要:
We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales, otherwise the value function is continuous. Moreover, we show the semi-group property (Bellman principle) and characterise the value function as a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of the optimal strategies change completely, depending on the amount of the trader's security holdings and where optimal strategies in the Black-Scholes type market with nonlinear market impact are not block liquidation but gradual liquidation, even when the trader is risk-neutral.
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PDF链接:
https://arxiv.org/pdf/0907.3282