P-Bubbles, Q-Bubbles, and Risk Premia

Robert Jarrow () and Simon S. Kwok

Papers from arXiv.org

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.

Date: 2026-08
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