Rational Belief Bubbles - Sohn, Hyun-U; Sornette, Didier (Frontiers in Physics, 2020)
We propose an extension of the class of rational expectations bubbles (REBs) to the more general rational beliefs setting of [1, 2]. In a potentially non-stationary but stationarizable environment, among a heterogenous population of agents, it is possible to hold more than one “rational” expectation. When rational but diverse beliefs converge (“correlated beliefs”), they do not cancel each other out in aggregate anymore. This can make them an object of rational speculation. Accounting for the fact that market efficiency has an intrinsic time-dimension, we show that diverse but correlated beliefs can thus account for speculative bubbles, without the need for irrational agents or limits to arbitrage. Many of the shortcomings of REBs that make rational bubbles implausible can be overcome once we relax the ergodicity requirement. In particular, we argue that the hitherto unexplained “bubble component” of REBs corresponds to the extension of the state space in [3].