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

Salvador Cruz Rambaud; Blas Torrecillas Jover; Salvador Cruz Rambaud; Blas Torrecillas Jover

doi:10.3934/math.2022575

AIMS Mathematics

2022, Volume 7, Issue 6: 10315-10343. doi: 10.3934/math.2022575

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Research article

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

Salvador Cruz Rambaud ^{1
,
,},
Blas Torrecillas Jover ²

1.
Departamento de Economía y Empresa. Universidad de Almería, La Cañada de San Urbano, s/n, 04120, Almería, Spain
2.
Departamento de Matemáticas. Universidad de Almería, La Cañada de San Urbano, s/n, 04120, Almería, Spain

Received: 19 November 2021 Revised: 07 February 2022 Accepted: 01 March 2021 Published: 24 March 2022
MSC : 91G99

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.
- intertemporal choice,
- discount function,
- additivity,
- vector space,
- affine space,
- quiver
Citation: Salvador Cruz Rambaud, Blas Torrecillas Jover. An analysis of the algebraic structures in the context of intertemporal choice[J]. AIMS Mathematics, 2022, 7(6): 10315-10343. doi: 10.3934/math.2022575

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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.

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