Strict local martingales and optimal investment in a Black–Scholes model with a bubble
dc.contributor.author | Herdegen, Martin | |
dc.contributor.author | Herrmann, Sebastian | |
dc.date.accessioned | 2019-01-15T20:29:50Z | |
dc.date.available | 2020-03-03T21:29:35Z | en |
dc.date.issued | 2019-01 | |
dc.identifier.citation | Herdegen, 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.issn | 0960-1627 | |
dc.identifier.issn | 1467-9965 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/147103 | |
dc.description.abstract | There 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.publisher | Birkhäuser | |
dc.publisher | Wiley Periodicals, Inc. | |
dc.subject.other | utility maximization | |
dc.subject.other | power utility | |
dc.subject.other | strict local martingales | |
dc.subject.other | optimal investment | |
dc.subject.other | bubbles | |
dc.subject.other | JLS model | |
dc.title | Strict local martingales and optimal investment in a Black–Scholes model with a bubble | |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | |
dc.subject.hlbsecondlevel | Mathematics | |
dc.subject.hlbsecondlevel | Finance | |
dc.subject.hlbtoplevel | Science | |
dc.subject.hlbtoplevel | Business and Economics | |
dc.description.peerreviewed | Peer Reviewed | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/147103/1/mafi12175_am.pdf | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/147103/2/mafi12175.pdf | |
dc.identifier.doi | 10.1111/mafi.12175 | |
dc.identifier.source | Mathematical Finance | |
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dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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