Basis of Financial Arithmetic from the Point View of the Utility Theory

Abstract

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