Asset price bubbles in markets with transaction costs

Abstract

<p style="text-indent:20px;">We study asset price bubbles in market models with proportional transaction costs <inline-formula><tex-math id="M1">\begin{document}$ \lambda\in (0, 1) $\end{document}</tex-math></inline-formula> and finite time horizon <inline-formula><tex-math id="M2">\begin{document}$ T $\end{document}</tex-math></inline-formula> in the setting of [<xref ref-type="bibr" rid="b49">49</xref>]. By following [<xref ref-type="bibr" rid="b29">29</xref>], we define the fundamental value <inline-formula><tex-math id="M3">\begin{document}$ F $\end{document}</tex-math></inline-formula> of a risky asset <inline-formula><tex-math id="M4">\begin{document}$ S $\end{document}</tex-math></inline-formula> as the price of a super-replicating portfolio for a position terminating in one unit of the asset and zero cash. We then obtain a dual representation for the fundamental value by using the super-replication theorem of [<xref ref-type="bibr" rid="b50">50</xref>]. We say that an asset price has a bubble if its fundamental value differs from the ask-price <inline-formula><tex-math id="M5">\begin{document}$ (1+\lambda)S $\end{document}</tex-math></inline-formula>. We investigate the impact of transaction costs on asset price bubbles and show that our model intrinsically includes the birth of a bubble.</p>