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Strong bubbles and strict local martingales
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Herdegen, Martin and Schweizer, Martin (2016) Strong bubbles and strict local martingales. International Journal of Theoretical and Applied Finance, 19 (4). 1650022. doi:10.1142/S0219024916500229 ISSN 0219-0249.
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Official URL: http://dx.doi.org/10.1142/S0219024916500229
Abstract
In a numéraire-independent framework, we study a financial market with NN assets which are all treated in a symmetric way. We define the fundamental value ∗S of an asset SS as its super-replication price and say that the market has a strong bubble if ∗S and SS deviate from each other. None of these concepts needs any mention of martingales. Our main result then shows that under a weak absence-of-arbitrage assumption (basically NUPBR), a market has a strong bubble if and only if in all numéraire s for which there is an equivalent local martingale measure (ELMM), asset prices are strict local martingales under all possible ELMMs. We show by an example that our bubble concept lies strictly between the existing notions from the literature. We also give an example where asset prices are strict local martingales under one ELMM, but true martingales under another, and we show how our approach can lead naturally to endogenous bubble birth.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Journal or Publication Title: | International Journal of Theoretical and Applied Finance | ||||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||
ISSN: | 0219-0249 | ||||||
Official Date: | June 2016 | ||||||
Dates: |
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Volume: | 19 | ||||||
Number: | 4 | ||||||
Article Number: | 1650022 | ||||||
DOI: | 10.1142/S0219024916500229 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access |
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