  In this paper we see the evolution of a capitalized financial event e, with
respect to a capitalization factor f, as the exponential map of a suitably
defined Lie group G(f,e), supported by the half-space of capitalized financial
events having the same capital sign of e. The Lie group G(f,e) depends upon the
capitalization factor f and on the event e itself. After the extension of the
definition of exponential map of a Lie group, we shall eliminate the dependence
on the financial event e, recognizing the presence of essentially one unique
financial Lie semigroup, supported by the entire space of capitalized financial
events, determined by the capitalization factor f.
