P-Bubbles, Q-Bubbles, and Risk Premia
Mathematical Finance
2026-08-03 v1 Theoretical Economics
Abstract
We develop a unified modeling framework that connects two distinct types of bubbles defined in the literature: the rational bubbles (aka P-bubbles), and the local martingale bubbles (aka Q-bubbles). We show that the local martingale bubble model includes the classical rational bubble as a special case. We relate both types of bubbles to an equity's risk premium via a novel decomposition.
Cite
@article{arxiv.2608.01554,
title = {P-Bubbles, Q-Bubbles, and Risk Premia},
author = {Robert A. Jarrow and Simon S. Kwok},
journal= {arXiv preprint arXiv:2608.01554},
year = {2026}
}