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Model-free CPPI

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  • Alexander Schied
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    Abstract

    We consider Constant Proportion Portfolio Insurance (CPPI) and its dynamic extension, which may be called Dynamic Proportion Portfolio Insurance (DPPI). It is shown that these investment strategies work within the setting of F\"ollmer's pathwise It\^o calculus, which makes no probabilistic assumptions whatsoever. This shows, on the one hand, that CPPI and DPPI are completely independent of any choice of a particular model for the dynamics of asset prices. They even make sense beyond the class of semimartingale sample paths and can be successfully defined for models admitting arbitrage, including some models based on fractional Brownian motion. On the other hand, the result can be seen as a case study for the general issue of robustness in the face of model uncertainty in finance.

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    File URL: http://arxiv.org/pdf/1305.5915
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    Paper provided by arXiv.org in its series Papers with number 1305.5915.

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    Date of creation: May 2013
    Date of revision: Jan 2014
    Handle: RePEc:arx:papers:1305.5915

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    1. Louis Paulot & Xavier Lacroze, 2011. "One-Dimensional Pricing of CPPI," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(3), pages 207-225.
    2. Bick, Avi & Willinger, Walter, 1994. "Dynamic spanning without probabilities," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 50(2), pages 349-374, April.
    3. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
    4. Rama Cont & Peter Tankov, 2009. "Constant Proportion Portfolio Insurance In The Presence Of Jumps In Asset Prices," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 19(3), pages 379-401.
    5. Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 11(3), pages 285-314.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
    8. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.
    9. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, Econometric Society, vol. 74(6), pages 1447-1498, November.
    10. Black, Fischer & Perold, AndreF., 1992. "Theory of constant proportion portfolio insurance," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 16(3-4), pages 403-426.
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