Lie group structures for financial evolutions

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 Gf,e, supported by the halfspace of capitalized financial events having the same sign of e. The Lie group Gf,e depends on the capitalization factor f and on the event e itself. After the extention of the definition of exponential map of a Lie group, we shall eliminate the dependence on the financial event e, recognizing the precence of essen- tialy one unique financial Lie semigroup, supported by the entire space of capitalized financial events, determined by the capitalization factor f.