Optimal Investment in a Black-Scholes Model with a Bubble

Martin Herdegen and Sebastian Herrmann
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Martin Herdegen: University of Warwick - Department of Statistics
Sebastian Herrmann: University of Michigan at Ann Arbor

No 13-58, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 which can be strict local martingales and which 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.

Keywords: Optimal investment; Utility maximization; Power utility; Black-Scholes model; Mean-variance; Bubbles; Financial crashes; Strict local martingales (search for similar items in EconPapers)
JEL-codes: G11 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2013-11
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp1358

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