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Projections of scaled bessel processes

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  • Kardaras, Constantinos
  • Ruf, Johannes

Abstract

Let X and Y denote two independent squared Bessel processes of dimension m and n-m, respectively, with n ≥ 2 and m ∈ [0, n), making X+Y a squared Bessel process of dimension n. For appropriately chosen function s, the process s(X + Y) is a local martingale. We study the representation and the dynamics of s(X + Y), projected on the filtration generated by X. This projection is a strict supermartingale if, and only if, m

Suggested Citation

  • Kardaras, Constantinos & Ruf, Johannes, 2019. "Projections of scaled bessel processes," LSE Research Online Documents on Economics 100939, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:100939
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    File URL: http://eprints.lse.ac.uk/100939/
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    Citations

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    Cited by:

    1. Francesca Biagini & Andrea Mazzon & Ari-Pekka Perkkiö, 2023. "Optional projection under equivalent local martingale measures," Finance and Stochastics, Springer, vol. 27(2), pages 435-465, April.
    2. Çetin, Umut & Larsen, Kasper, 2023. "Uniqueness in cauchy problems for diffusive real-valued strict local martingales," LSE Research Online Documents on Economics 118743, London School of Economics and Political Science, LSE Library.
    3. Umut Cetin & Kasper Larsen, 2020. "Uniqueness in Cauchy problems for diffusive real-valued strict local martingales," Papers 2007.15041, arXiv.org, revised May 2022.
    4. Constantinos Kardaras & Johannes Ruf, 2020. "Filtration shrinkage, the structure of deflators, and failure of market completeness," Finance and Stochastics, Springer, vol. 24(4), pages 871-901, October.

    More about this item

    Keywords

    bessel processes; filtering; local martingale; local time;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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