  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.
