The family of operators associated with a capitalization law

Abstract

In the present paper we conduct a deep study on some basic concepts offinancial mathematics, showing their analitic and geometric nature. We define the new concept of family of the capitalization factors of a capitalization. The main theorems of the paper are Let F be a capitalization law. Then F is strong if and only if the family of operators associated with F is an invertible one parameter family. Let F: R^3 -> R be a capitalization law, then F is separable if and only if the family of operators associated with F is a one parameter group.