  We study the effects of stochastic resetting on geometric Brownian motion
(GBM), a canonical stochastic multiplicative process for non-stationary and
non-ergodic dynamics. Resetting is a sudden interruption of a process such that
the dynamics is renewed intermittently. Quite surprisingly, although resetting
renders GBM stationary, the resulting process remains non-ergodic. We observe
three different long-time regimes: a quenched state, an unstable and a stable
annealed state depending on the resetting strength. Crucially, the regimes are
well separated by a self-averaging time period which can be minimized by an
optimal resetting rate. Our results can be useful to interpret data emanating
from stock market collapse or reconstitution of investment portfolios.
