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Basis of financial arithmetic from the viewpoint of the utility theory

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  • Krzysztof Piasecki

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. Proposed approach to financial arithmetic is based on the financial flow utility concept. This utility function is defined as linear extension of multicriteria comparison determined by the time preference and the capital preference. Then the present value is equal to 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 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.

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  • Krzysztof Piasecki, 2013. "Basis of financial arithmetic from the viewpoint of the utility theory," Papers 1302.0537, arXiv.org.
    • Handle: RePEc:arx:papers:1302.0537
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    6. Krzysztof M. Piasecki, 2011. "Effectiveness of securities with fuzzy probabilistic return," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(2), pages 65-78.
    7. Piasecki, Krzysztof, 2011. "Rozmyte zbiory probabilistyczne jako narzędzie finansów behawioralnych [Fuzzy Probabilistic Sets as a Tool for Behavioural Finance]," MPRA Paper 46218, University Library of Munich, Germany.
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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, 2019. "Sharpe’s Ratio for Oriented Fuzzy Discount Factor," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    4. 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.
    5. 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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