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.

Lie group structures for financial evolutions

CARFI', David
2011

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/1912809
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