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Strict local martingales and optimal investment in a Black-Scholes model with a bubble
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Herdegen, Martin and Herrmann, Sebastian (2019) Strict local martingales and optimal investment in a Black-Scholes model with a bubble. Mathematical Finance, 29 (1). pp. 285-328. doi:10.1111/mafi.12175
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Official URL: https://doi.org/10.1111/mafi.12175
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.
| Item Type: | Journal Article | ||||||||
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| Subjects: | H Social Sciences > HF Commerce Q Science > QA Mathematics |
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| Divisions: | Faculty of Science > Statistics | ||||||||
| Library of Congress Subject Headings (LCSH): | Financial crises -- Mathematical mdoels, Martingales (Mathematics) | ||||||||
| Journal or Publication Title: | Mathematical Finance | ||||||||
| Publisher: | Wiley-Blackwell Publishing, Inc. | ||||||||
| ISSN: | 0960-1627 | ||||||||
| Official Date: | January 2019 | ||||||||
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| Volume: | 29 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | pp. 285-328 | ||||||||
| DOI: | 10.1111/mafi.12175 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| RIOXX Funder/Project Grant: |
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| Open Access Version: |
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