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The basis of financial arithmetic from the viewpoint of utility theory

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  • Krzysztof Piasecki

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. Thiscutility 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.

Suggested Citation

  • Krzysztof Piasecki, 2012. "The basis of financial arithmetic from the viewpoint of utility theory," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(3), pages 37-53.
    • Handle: RePEc:wut:journl:v:3:y:2012:p:37-53:id:1044
    DOI: 10.5277/ord120303
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    Cited by:

    1. Krzysztof Piasecki & Anna Łyczkowska-Hanćkowiak, 2019. "Representation of Japanese Candlesticks by Oriented Fuzzy Numbers," Econometrics, MDPI, vol. 8(1), pages 1-24, December.
    2. Anna Łyczkowska-Hanćkowiak & Krzysztof Piasecki, 2018. "The present value of a portfolio of assets with present values determined by trapezoidal ordered fuzzy numbers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(2), pages 41-56.
    3. Anna Łyczkowska-Hanćkowiak & Aleksandra Wójcicka-Wójtowicz, 2023. "On portfolio analysis using oriented fuzzy numbers for the trade-related sector of the Warsaw Stock Exchange," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(4), pages 155-170.
    4. Anna Łyczkowska-Hanćkowiak, 2019. "Sharpe’s Ratio for Oriented Fuzzy Discount Factor," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    5. Piasecki Krzysztof, 2014. "Intuitionistic Assessment Of Behavioural Present Value," Folia Oeconomica Stetinensia, Sciendo, vol. 13(2), pages 49-62.
    6. Krzysztof Piasecki & Joanna Siwek, 2018. "The portfolio problem with present value modelled by a discrete trapezoidal fuzzy number," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(1), pages 57-74.

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