Detecting Strict Local Martingales

Abstract

A fundamental feature of the benchmark approach introduced in Chap. 1 is that it is formulated under the real world measure and uses the Growth Optimal Portfolio as the numéraire portfolio. Unlike the classical risk neutral paradigm, it does not require the existence of a risk neutral measure, which of course provides the modeler with more freedom. In fact, we suggest in Chap. 3 that the lack of an equivalent risk neutral measure can be a plausible feature of a financial market, especially when analyzing its history over long periods of time. In this chapter, we propose another class of processes for modeling the GOP, for which one can easily establish whether the processes allow for an equivalent risk neutral measure or not. We use an argument due to Sin to establish whether a particular model for the GOP allows for an equivalent martingale measure or not by studying the boundary behavior of the relevant continuous diffusion process. In this context, the results from Chap. 16 are extremely helpful, especially because they allow us to compute the relevant functionals explicitly.