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Closedness of some spaces of stochastic integrals

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1686)

Abstract

We consider an R d-valued continous semimartingale (X t ) t∃[0, T] , the space of processes G p = {θ · X | θ · X is a semimartingale in S p} and the space of their terminal values G P T . We give necessary and sufficient conditions for completeness of G P in the norm ∥(θ · X)* p and closedness of G P T in L p. These results are related to some problems in mathematical finance and have been given for p=2 in [DMSSS].

1991 Mathematics Subject Classification

  • 60H05
  • 90A09

Supported by “Fonds zur Förderung der wissenschaftlichen Forschung in Österreich”, Project Nr. P11544

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References

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© 1998 Springer-Verlag

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Grandits, P., Krawczyk, L. (1998). Closedness of some spaces of stochastic integrals. In: Azéma, J., Yor, M., Émery, M., Ledoux, M. (eds) Séminaire de Probabilités XXXII. Lecture Notes in Mathematics, vol 1686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101752

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  • DOI: https://doi.org/10.1007/BFb0101752

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64376-0

  • Online ISBN: 978-3-540-69762-6

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