{"title":"Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs","authors":"Martin Brown, Tomasz Zastawniak","doi":"10.1007/s10436-020-00367-z","DOIUrl":null,"url":null,"abstract":"<div><p>We show that the absence of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with values within the bid-ask intervals that satisfies the martingale property with respect to each of the measures. This extends Harrison and Pliska’s classical Fundamental Theorem of Asset Pricing to the case of combined fixed and proportional transaction costs.</p></div>","PeriodicalId":45289,"journal":{"name":"Annals of Finance","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s10436-020-00367-z","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Finance","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s10436-020-00367-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
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Abstract
We show that the absence of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with values within the bid-ask intervals that satisfies the martingale property with respect to each of the measures. This extends Harrison and Pliska’s classical Fundamental Theorem of Asset Pricing to the case of combined fixed and proportional transaction costs.
期刊介绍：
Annals of Finance provides an outlet for original research in all areas of finance and its applications to other disciplines having a clear and substantive link to the general theme of finance. In particular, innovative research papers of moderate length of the highest quality in all scientific areas that are motivated by the analysis of financial problems will be considered. Annals of Finance''s scope encompasses - but is not limited to - the following areas: accounting and finance, asset pricing, banking and finance, capital markets and finance, computational finance, corporate finance, derivatives, dynamical and chaotic systems in finance, economics and finance, empirical finance, experimental finance, finance and the theory of the firm, financial econometrics, financial institutions, mathematical finance, money and finance, portfolio analysis, regulation, stochastic analysis and finance, stock market analysis, systemic risk and financial stability. Annals of Finance also publishes special issues on any topic in finance and its applications of current interest. A small section, entitled finance notes, will be devoted solely to publishing short articles – up to ten pages in length, of substantial interest in finance. Officially cited as: Ann Finance
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