Philip Protter
Modelling Financial Bubbles, Local Martingales and Filtration
Shrinkage
The mathematical modeling of financial bubbles involves subtle
distinctions between types of martingales and strict local martingales.
We will discuss how one can obtain the birth of a bubble through the
market's shifting choices of risk neutral measures. The presence of
bubbles leads to some conventional wisdom being false, such as "no
early exercise" with American call options. Once the role of local
martingales becomes clear, we show how perversely local martingales can
behave through reductions of information levels (filtration shrinkage).