A note on stochastic integration with respect to optional semimartingales.
Kühn, Christoph, Stroh, Maximilian (2009)
Electronic Communications in Probability [electronic only]
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Kühn, Christoph, Stroh, Maximilian (2009)
Electronic Communications in Probability [electronic only]
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Jia-An Yan (1991)
Séminaire de probabilités de Strasbourg
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Norihiko Kazamaki (1971)
Annales de l'I.H.P. Probabilités et statistiques
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Adam Osękowski (2010)
Bulletin of the Polish Academy of Sciences. Mathematics
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Hyungsok Ahn, Philip Protter (1994)
Séminaire de probabilités de Strasbourg
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Peter Imkeller (1989)
Séminaire de probabilités de Strasbourg
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Francis Hirsch, Bernard Roynette (2012)
ESAIM: Probability and Statistics
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In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
Watanabe, Shinzo (2009)
Journal Électronique d'Histoire des Probabilités et de la Statistique [electronic only]
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Darrell Duffie (1985)
Séminaire de probabilités de Strasbourg
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F. Utzet (1985)
Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
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Jiří Witzany (2017)
Commentationes Mathematicae Universitatis Carolinae
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The concept of an equivalent martingale measure is of key importance for pricing of financial derivative contracts. The goal of the paper is to apply infinitesimals in the non-standard analysis set-up to provide an elementary construction of the equivalent martingale measure built on hyperfinite binomial trees with infinitesimal time steps.