Submartingale in Bitcoin Prices

Abstract

We consider an economy endowed with two rival currencies: Dollar and Bitcoin, both of which inherently carry no value at all. While the Dollar is maintained by the U.S. Fed with target inflation, the supply in Bitcoin tapers to zero over time. We present a model with underlying pricing equations that a submartingale prevails on Bitcoin prices. Hence, Bitcoin prices appreciate over time. Absence of mutual impatience in Dollars leads to Bitcoin speculation. The main source of Bitcoin appreciation comes from the high inflation in Dollar over that in Bitcoin. We also show Bitcoin speculation and equilibrium to Bitcoin persistence over competing with Dollars.