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Strict local martingales and optimal investment in a Black–Scholes model with a bubble
dc.contributor.authorHerdegen, Martin
dc.contributor.authorHerrmann, Sebastian
dc.date.accessioned2019-01-15T20:29:50Z
dc.date.available2020-03-03T21:29:35Zen
dc.date.issued2019-01
dc.identifier.citationHerdegen, Martin; Herrmann, Sebastian (2019). "Strict local martingales and optimal investment in a Black–Scholes model with a bubble." Mathematical Finance 29(1): 285-328.
dc.identifier.issn0960-1627
dc.identifier.issn1467-9965
dc.identifier.urihttps://hdl.handle.net/2027.42/147103
dc.description.abstractThere are two major streams of literature on the modeling of financial bubbles: the strict local martingale framework and the Johansen–Ledoit–Sornette (JLS) financial bubble model. Based on a class of models that embeds the JLS model and can exhibit strict local martingale behavior, we clarify the connection between these previously disconnected approaches. While the original JLS model is never a strict local martingale, there are relaxations that can be strict local martingales and that preserve the key assumption of a log‐periodic power law for the hazard rate of the time of the crash. We then study the optimal investment problem for an investor with constant relative risk aversion in this model. We show that for positive instantaneous expected returns, investors with relative risk aversion above one always ride the bubble.
dc.publisherBirkhäuser
dc.publisherWiley Periodicals, Inc.
dc.subject.otherutility maximization
dc.subject.otherpower utility
dc.subject.otherstrict local martingales
dc.subject.otheroptimal investment
dc.subject.otherbubbles
dc.subject.otherJLS model
dc.titleStrict local martingales and optimal investment in a Black–Scholes model with a bubble
dc.typeArticleen_US
dc.rights.robotsIndexNoFollow
dc.subject.hlbsecondlevelMathematics
dc.subject.hlbsecondlevelFinance
dc.subject.hlbtoplevelScience
dc.subject.hlbtoplevelBusiness and Economics
dc.description.peerreviewedPeer Reviewed
dc.description.bitstreamurlhttps://deepblue.lib.umich.edu/bitstream/2027.42/147103/1/mafi12175_am.pdf
dc.description.bitstreamurlhttps://deepblue.lib.umich.edu/bitstream/2027.42/147103/2/mafi12175.pdf
dc.identifier.doi10.1111/mafi.12175
dc.identifier.sourceMathematical Finance
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dc.owningcollnameInterdisciplinary and Peer-Reviewed


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