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Financial Decisions Based on Zero-Sum Games: New Conceptual and Mathematical Outcomes

Author

Listed:
  • Pierpaolo Angelini

    (Dipartimento di Scienze Statistiche, Università La Sapienza, 00185 Rome, Italy)

Abstract

All the n possible returns on a financial asset are the components of an element of a linear space over R . This paper shows how to transfer all these n possible returns on a one-dimensional straight line. In this research work, two or more than two financial assets are studied. More than two financial assets are always studied in pairs, so they are treated inside the budget set of a given decision-maker. Two univariate financial assets give rise to a bivariate financial asset characterized by a bivariate (two-dimensional) distribution of probability. This research work shows how constrained choices being made by a given decision-maker under conditions of uncertainty and riskiness maximize his utility of an ordinal nature. For this reason, prevision bundles are dealt with. Furthermore, every choice identifies a zero-sum game. Since a specific kind of choice associated with two or more than two objects is investigated, new conceptual and mathematical outcomes related to financial decisions are shown.

Suggested Citation

  • Pierpaolo Angelini, 2024. "Financial Decisions Based on Zero-Sum Games: New Conceptual and Mathematical Outcomes," IJFS, MDPI, vol. 12(2), pages 1-28, June.
    • Handle: RePEc:gam:jijfss:v:12:y:2024:i:2:p:56-:d:1415064
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    References listed on IDEAS

    as
    1. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60(2), pages 151-151.
    2. Pierpaolo Angelini, 2024. "Invariance of the Mathematical Expectation of a Random Quantity and Its Consequences," Risks, MDPI, vol. 12(1), pages 1-17, January.
    3. Federico Echenique, 2020. "New Developments in Revealed Preference Theory: Decisions Under Risk, Uncertainty, and Intertemporal Choice," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 299-316, August.
    4. Steven D. Levitt, 2004. "Why are gambling markets organised so differently from financial markets?," Economic Journal, Royal Economic Society, vol. 114(495), pages 223-246, April.
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    Cited by:

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    2. Nadezhda Yarushkina & Aleksey Filippov & Anton Romanov, 2024. "Contextual Analysis of Financial Time Series," Mathematics, MDPI, vol. 13(1), pages 1-17, December.

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