{"title":"Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies","authors":"Ulrich Horst, Evgueni Kivman","doi":"10.1007/s00780-024-00536-2","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"32 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finance and Stochastics","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s00780-024-00536-2","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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