Framework and justification: The content of this paper is located on the intersection of two fields: Finance and Algebra. In effect, the current dynamism shown by most financial instruments makes it necessary to endow the foundations of finance with, as general as possible, algebraic structures. Therefore, the objective of this paper is to provide a novel view of the fundamentals of finance by using purely algebraic concepts and structures, more specifically the properties of separability and additivity of the involved discount functions and their corresponding operators. This approach provides more flexibility to the axioms of financial mathematics, so anticipating potential changes in the behavior of the so-called "rational" decision makers. Methodologically, this paper uses a variety of algebraic tools which fit the intuition behind the financial logic. Indeed, the main contribution of the paper is the wide variety of algebraic concepts belonging to the abstract algebra which can be applied to describe the behavior of intertemporal choices.

The framework of this paper is behavioral finance and, more specifically, intertemporal choice when individuals exhibit decreasing impatience in their decision-making processes. After characterizing the two main types of decreasing impatience (moderately and strongly decreasing impatience), the main objective of this paper is to generalize these concepts when the criterion of time increase is given by an arbitrary function which describes such increments. In general, the methodology is mathematical calculus but particularly the concept of derivative according to the function which rules the increase of time. The main contribution of this paper is the characterization of this extension of the concept of decreasing impatience by using the aforementioned novel derivative and the well-known Prelec's index.