Model-free CPPI |
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| Institution: | 1. Faculty of Mathematics, “Alexandru Ioan Cuza” University of Iaşi, Iaşi 700506, Romania;2. “Octav Mayer” Institute of Mathematics of the Romanian Academy, Iaşi 700506, Romania;3. ADAMSS (Advanced Applied Mathematical and Statistical Sciences), Universitá degli Studi di Milano, 20133 Milano, Italy;4. Department of Mathematics, Universitá degli Studi di Milano, 20133 Milano, Italy;1. European Commission, DG Joint Research Centre (JRC), Institute for the Protection and Security of the Citizen (IPSC), Via E. Fermi 2749, 21027 Ispra (VA), Italy;2. CNR, Istituto di Matematica Applicata e Tecnologie Informatiche “Enrico Magenes”, Via E. Bassini 15, 20133 Milano, Italy;1. Institut Jacques Monod, CNRS UMR 7592, Univ Paris Diderot, Paris Cité Sorbonne, F-750205 Paris, France;2. Max Planck Research Group on ‘Modeling the Evolution of Aging’, 18057 Rostock, Germany;1. Department of Statistics & Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou str. T. K. 18534 Piraeus, Greece;2. Actuarial Research Group, KU Leuven, Naamsestraat 69, B-3000 Leuven, Belgium;1. School of Mathematics and Statistics, University of New South Wales, NSW 2052, Australia;2. Finance Discipline Group and School of Mathematical and Physical Sciences, University of Technology Sydney, PO Box 123, Broadway, NSW 2007, Australia |
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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 Föllmer's pathwise Itô calculus, which makes no probabilistic assumptions whatsoever. This shows, on 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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| Keywords: | CPPI DPPI Model uncertainty Knightian uncertainty Föllmer's pathwise Itô calculus Robustness Pathwise trading strategies |
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