Taxa de juros instantânea e a capitalização contínua aplicadas ás funções atuariais de sobrevivência

Abstract

This paper presents the continuous compounding financial regime and applies it to the principal classical survival functions (de Moivre, Gompertz–Makeham, exponential, and Weibull). To this end, it develops the underlying theory through a bibliographic review, starting from introductory concepts like simple interest, compound interest, proportional rates, equivalent rates, nominal and effective interest rates, to build the mathematical foundations for instantaneous, or continuous, interest rates and the corresponding continuous compounding regime. It first presents basic and general notions of these models, followed by an exploration of their specific characteristics and their relation to continuous compounding. Notably, the models addressed offer theoretical descriptions of behaviors, such as population mortality or cumulative functions.