在市场影响较小和投资组合清算的情况下，利用半鞅策略实现最优交易执行

IF 1.1 2区经济学 Q3 BUSINESS, FINANCE

Finance and Stochastics Pub Date : 2024-06-14 DOI:10.1007/s00780-024-00536-2

Ulrich Horst, Evgueni Kivman

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引用次数: 0

摘要

我们考虑的是一个具有瞬时价格影响和小瞬时影响因子随机弹性的最优清算问题。在我们的建模框架内，当瞬时影响因子趋近于零时，最优投资组合过程会收敛到具有一般半鞅控制的最优清算问题的解。我们的结果提供了一个统一的框架，可将清算文献中最常用的两个建模框架嵌入其中，并为使用半鞅清算策略和使用无约束变化的投资组合过程奠定了基础。我们的收敛结果基于具有奇异终点条件的 BSDE 的新收敛结果，以及 BSDE 在前向过程的均匀连续函数方面的新表示结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies

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Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies

We consider an optimal liquidation problem with instantaneous price impact and stochastic resilience for small instantaneous impact factors. Within our modelling framework, the optimal portfolio process converges to the solution of an optimal liquidation problem with general semimartingale controls when the instantaneous impact factor converges to zero. Our results provide a unified framework within which to embed the two most commonly used modelling frameworks in the liquidation literature and provide a foundation for the use of semimartingale liquidation strategies and the use of portfolio processes of unbounded variation. Our convergence results are based on novel convergence results for BSDEs with singular terminal conditions and novel representation results of BSDEs in terms of uniformly continuous functions of forward processes.

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来源期刊

Finance and Stochastics 管理科学-数学跨学科应用

CiteScore

2.90

自引率

5.90%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Finance and Stochastics is to provide a high standard publication forum for research - in all areas of finance based on stochastic methods - on specific topics in mathematics (in particular probability theory, statistics and stochastic analysis) motivated by the analysis of problems in finance. Finance and Stochastics encompasses - but is not limited to - the following fields: - theory and analysis of financial markets - continuous time finance - derivatives research - insurance in relation to finance - portfolio selection - credit and market risks - term structure models - statistical and empirical financial studies based on advanced stochastic methods - numerical and stochastic solution techniques for problems in finance - intertemporal economics, uncertainty and information in relation to finance.