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Hobson, David G. (2016) Mimicking martingales. Annals of Applied Probability, 26 (4). pp. 2273-2303. 1472745459. doi:10.1214/15-AAP1147 ISSN 1050-5164.
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Official URL: http://dx.doi.org/10.1214/15-AAP1147
Abstract
Given the univariate marginals of a real-valued, continuous-time martingale, (respectively, a family of measures parameterised by t∈[0,T] which is increasing in convex order, or a double continuum of call prices) we construct a family of pure-jump martingales which mimic that martingale (respectively, are consistent with the family of measures, or call prices). As an example, we construct a fake Brownian motion. Then, under a further `dispersion' assumption, we construct the martingale which (within the family of martingales which are consistent with a given set of measures) has the smallest expected total variation. We also give a path-wise inequality, which in the mathematical finance context yields a model-independent sub-hedge for an exotic security with payoff equal to the total variation along a realisation of the price process.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Martingales (Mathematics) | ||||||||
Journal or Publication Title: | Annals of Applied Probability | ||||||||
Publisher: | Institute of Mathematical Statistics | ||||||||
ISSN: | 1050-5164 | ||||||||
Official Date: | August 2016 | ||||||||
Dates: |
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Volume: | 26 | ||||||||
Number: | 4 | ||||||||
Page Range: | pp. 2273-2303 | ||||||||
Article Number: | 1472745459 | ||||||||
DOI: | 10.1214/15-AAP1147 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 25 May 2016 | ||||||||
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