The Basis of Financial Arithmetic from the Viewpoint of Utility Theory

Abstract

The main goal of this paper is to present a modern axiomatic approach to financial arithmetic. An axiomatic theory of financial arithmetic was first proposed by Peccati, who introduced an axiomatic definition of future value. This theory has been extensively developed in recent years. The proposed approach to financial arithmetic is based on the concept of the utility of a financial flow. This utility function is defined as a linear extension of a multicriterion comparison determined by an individual's time preference and capital preference. The present value is then defined to be the utility of the financial flow. Therefore, the law of the diminishing marginal utility of wealth has been considered as an additional feature of the present value. The future value is defined as the inverse of the utility function. This definition is a generalization of Peccati's one. The net present value is given as the unique additive extension of the utility of the financial flow. Moreover, the synergy effect and the diversification effect will be discussed. At the end, the axiomatic definition of the present value will be specified in three ways. (original abstract)