Arbitrage of the first kind and filtration enlargements in semimartingale financial models

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• 作者：Beatrice Acciaio^a ; ^{b.acciaio@lse.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Claudio Fontana^b ; ^{fontana@math.univ-paris-diderot.fr" class="auth_mail" title="E-mail the corresponding author} ; Constantinos Kardaras^a ; ^{k.kardaras@lse.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60G44 ; 91G10
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：126
• 期：6
• 页码：1761-1784
• 全文大小：324 K

文摘

In a general semimartingale financial model, we study the stability of the No Arbitrage of the First Kind   (class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S030441491500321X&_mathId=si1.gif&_user=111111111&_pii=S030441491500321X&_rdoc=1&_issn=03044149&md5=be3e240a924408ea43e84590ee3d2303">class="imgLazyJSB inlineImage" height="11" width="27" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S030441491500321X-si1.gif">class="mathContainer hidden">class="mathCode">${\mathrm{NA}}_1$) (or, equivalently, No Unbounded Profit with Bounded Risk) condition under initial and under progressive filtration enlargements. In both cases, we provide a simple and general condition which is sufficient to ensure this stability for any fixed   semimartingale model. Furthermore, we give a characterisation of the class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S030441491500321X&_mathId=si1.gif&_user=111111111&_pii=S030441491500321X&_rdoc=1&_issn=03044149&md5=be3e240a924408ea43e84590ee3d2303">class="imgLazyJSB inlineImage" height="11" width="27" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S030441491500321X-si1.gif">class="mathContainer hidden">class="mathCode">${\mathrm{NA}}_1$ stability for all semimartingale models.