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Proofs for the New Definitions in Financial Markets

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  • Atilla Aras

Abstract

Constructing theorems can help to determine the shape of certain utility curves that make up the new definitions in financial markets. The aim of this study was to present proofs for these theorems. Basic thoughts of new alternative definitions emerge from the decision-making under uncertainty in economics and finance. Shape of the certain utility curve is central to standard definitions in determining risk attitudes of investors. Shape alone determines risk behavior of investors in standard theory. Although the terms risk-averse, risk-loving, and risk-neutral are equivalent to strict concavity, strict convexity, and linearity, respectively, in standard theory, strict concavity or strict convexity, or linearity are valid for certain new definitions, not being the same as standard theory. Hence, it can be stated that new alternative definitions are broader than standard definitions from the viewpoint of shape. For instance, the certain utility curve of a risk-averse investor can be strictly concave or strictly convex, or linear in alternative definitions.

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  • Atilla Aras, 2023. "Proofs for the New Definitions in Financial Markets," Papers 2309.03003, arXiv.org, revised May 2024.
    • Handle: RePEc:arx:papers:2309.03003
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    1. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    2. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    3. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    4. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
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