  Recent advances in the development of artificial intelligence, technological
progress acceleration, long-term trends of macroeconomic dynamics increase the
relevance of technological singularity hypothesis. In this paper, we build a
model of finite-time technological singularity assuming that artificial
intelligence will replace humans for artificial intelligence engineers after
some point in time when it is developed enough. This model implies the
following: let A be the level of development of artificial intelligence. Then,
the moment of technological singularity n is defined as the point in time where
artificial intelligence development function approaches infinity. Thus, it
happens in finite time. Although infinite level of development of artificial
intelligence cannot be reached practically, this approximation is useful for
several reasons, firstly because it allows modeling a phase transition or a
change of regime. In the model, intelligence growth function appears to be
hyperbolic function under relatively broad conditions which we list and
compare. Subsequently, we also add a stochastic term (Brownian motion) to the
model and investigate the changes in its behavior. The results can be applied
for the modeling of dynamics of various processes characterized by
multiplicative growth.
