We present a dynamic Rational Expectations (RE) bubble model of prices with the intention to evaluate it on optimal … investment strategies applied to Bitcoin. Our bubble model is defined as a geometric Brownian motion combined with separate crash … (and rally) discrete jump distributions associated with positive (and negative) bubbles. The RE condition implies that the …

, abnormally high asset prices can be caused by financial bubbles. In this model, bubbles can emerge and deflate both in cycles or … rate. This can lead to new stable equilibria, but the emergence and bursting of bubbles cannot be prevented. …

Galí (2014) showed that a monetary policy rule that raises interest rates in response to bubbles can paradoxically lead … to larger bubbles. This comment shows that a central bank that wants to dampen bubbles can always do so by raising … argue Galí's model contains additional equilibria in which more aggressive rules dampen bubbles. We show that for these …