An analysis of the algebraic structures in the context of intertemporal choice

Abstract

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.

Keywords

• intertemporal choice
• discount function
• additivity
• vector space
• affine space
• quiver