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Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples

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  • Karen Grigorian
  • Robert A. Jarrow

Abstract

In this paper we provide an exhaustive survey of the current state of the mathematics of filtration enlargement and an interpretation of the key results of the literature from the viewpoint of mathematical finance. The emphasis is on providing a well-structured compendium of known mathematical results that can be used by researchers in mathematical finance. We mainly state the results and discuss their role and significance, with references provided for the omitted proofs. The discussion of mathematical results is accompanied by numerous examples from mathematical finance.

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  • Karen Grigorian & Robert A. Jarrow, 2023. "Enlargement of Filtrations: An Exposition of Core Ideas with Financial Examples," Papers 2303.03573, arXiv.org.
    • Handle: RePEc:arx:papers:2303.03573
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    References listed on IDEAS

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    1. Ernst, Philip A. & Rogers, L.C.G. & Zhou, Quan, 2017. "The value of foresight," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3913-3927.
    2. Jeanblanc, Monique & Song, Shiqi, 2015. "Martingale representation property in progressively enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4242-4271.
    3. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 263-286, July.
    4. D'Auria, Bernardo & Salmerón Garrido, José Antonio, 2019. "Insider information and its relation with the arbitrage condition and the utility maximization problem," DES - Working Papers. Statistics and Econometrics. WS 28805, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Di Tella, Paolo, 2020. "On the weak representation property in progressively enlarged filtrations with an application in exponential utility maximization," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 760-784.
    6. Dorte Kreher, 2013. "Change of measure up to a random time: Details," Papers 1309.6141, arXiv.org, revised Aug 2016.
    7. Imkeller, Peter, 2001. "Random times at which insiders can have free lunches," SFB 373 Discussion Papers 2001,62, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Jeanblanc, Monique & Song, Shiqi, 2011. "An explicit model of default time with given survival probability," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1678-1704, August.
    9. Fontana, Claudio & Grbac, Zorana & Jeanblanc, Monique & Li, Qinghua, 2014. "Information, no-arbitrage and completeness for asset price models with a change point," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3009-3030.
    10. Claudio Fontana, 2015. "The strong predictable representation property in initially enlarged filtrations under the density hypothesis," Papers 1508.03282, arXiv.org, revised Jun 2017.
    11. Claudio Fontana, 2013. "Weak and strong no-arbitrage conditions for continuous financial markets," Papers 1302.7192, arXiv.org, revised May 2014.
    12. Peter Imkeller & Nicolas Perkowski, 2011. "The Existence of Dominating Local Martingale Measures," Papers 1111.3885, arXiv.org, revised Mar 2013.
    13. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    14. Beatrice Acciaio & Claudio Fontana & Constantinos Kardaras, 2014. "Arbitrage of the first kind and filtration enlargements in semimartingale financial models," Papers 1401.7198, arXiv.org, revised May 2015.
    15. Claudio Fontana & Zorana Grbac & Monique Jeanblanc & Qinghua Li, 2013. "Information, no-arbitrage and completeness for asset price models with a change point," Papers 1304.0923, arXiv.org, revised Apr 2014.
    16. Ngoc Huy Chau & Wolfgang Runggaldier & Peter Tankov, 2016. "Arbitrage and utility maximization in market models with an insider," Papers 1608.02068, arXiv.org, revised Sep 2016.
    17. Medvegyev, Peter, 2007. "Stochastic Integration Theory," OUP Catalogue, Oxford University Press, number 9780199215256.
    18. Amendinger, Jürgen & Imkeller, Peter & Schweizer, Martin, 1998. "Additional logarithmic utility of an insider," SFB 373 Discussion Papers 1998,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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