Model-free CPPI

TL;DR

This paper demonstrates that CPPI and DPPI investment strategies are model-free, valid under Föllmer's pathwise Itô calculus, and applicable even in arbitrage models, highlighting their robustness against model uncertainty.

Contribution

It introduces a model-free framework for CPPI and DPPI strategies using pathwise calculus, extending their validity beyond traditional stochastic models.

Findings

Strategies are valid without probabilistic assumptions.

Applicable to models with arbitrage and fractional Brownian motion.

Highlights robustness of investment strategies under model uncertainty.

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.