41,833 research outputs found

    Reflections on Mathematical Economics in the Algorithmic Mode

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    Non-standard analysis can be harnessed by the recursion theorist. But as a computable economist, the conundrums of the Löwenheim-Skolem theorem and the associated Skolem paradox, seem to pose insurmountable epistemological difficulties against the use of algorithmic non-standard analysis. Discontinuities can be tamed by recursive analysis. This particular kind of taming may be a way out of the formidable obstacles created by the difficulties of Diophantine Decision Problems. Methods of existence proofs, used by the classical mathematician - even if not invoking the axiom of choice - cannot be shown to be equivalent to the exhibition of an instance in the sense of a constructive proof. These issues were prompted by the fertile and critical contributions to this special issue.

    Graduate Catalog, 2005-2006

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    https://scholar.valpo.edu/gradcatalogs/1032/thumbnail.jp

    The effect of multidisciplinary collaborations on research diversification

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    This work verifies whether research diversification by a scientist is in some measure related to their collaboration with multidisciplinary teams. The analysis considers the publications achieved by 5300 Italian academics in the sciences over the period 2004-2008. The findings show that a scientist's outputs resulting from research diversification are more often than not the result of collaborations with multidisciplinary teams. The effect becomes more pronounced with larger and particularly with more diversified teams. This phenomenon is observed both at the overall level and for the disciplinary macro-areas

    Innovation and Equilibrium?

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    Graduate Catalog, 2002-2003

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    https://scholar.valpo.edu/gradcatalogs/1029/thumbnail.jp

    Innovation and Equilibrium?

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    A discussion is given of the problems involved in the formal modeling of the innovation process. The link between innovation and finance is stressed. The nature of how the circular flow of funds is broken and the role of finance in evaluation and control is discussed.Innovation, Invention, Circular flow, Finance

    Determination of Risk Pricing Measures from Market Prices of Risk

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    A new insurance provider or a regulatory agency may be interested in determining a risk measure consistent with observed market prices of a collection of risks. Using a relationship between distorted coherent risk measures and spectral risk measures, we provide a method for reconstruction distortion functions from the observed prices of risk. The technique is based on an appropriate application of the method on maximum entropy in the mean.

    Computability and Algorithmic Complexity in Economics

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    This is an outline of the origins and development of the way computability theory and algorithmic complexity theory were incorporated into economic and finance theories. We try to place, in the context of the development of computable economics, some of the classics of the subject as well as those that have, from time to time, been credited with having contributed to the advancement of the field. Speculative thoughts on where the frontiers of computable economics are, and how to move towards them, conclude the paper. In a precise sense - both historically and analytically - it would not be an exaggeration to claim that both the origins of computable economics and its frontiers are defined by two classics, both by Banach and Mazur: that one page masterpiece by Banach and Mazur ([5]), built on the foundations of Turing’s own classic, and the unpublished Mazur conjecture of 1928, and its unpublished proof by Banach ([38], ch. 6 & [68], ch. 1, #6). For the undisputed original classic of computable economics is Rabinís effectivization of the Gale-Stewart game ([42];[16]); the frontiers, as I see them, are defined by recursive analysis and constructive mathematics, underpinning computability over the computable and constructive reals and providing computable foundations for the economist’s Marshallian penchant for curve-sketching ([9]; [19]; and, in general, the contents of Theoretical Computer Science, Vol. 219, Issue 1-2). The former work has its roots in the Banach-Mazur game (cf. [38], especially p.30), at least in one reading of it; the latter in ([5]), as well as other, earlier, contributions, not least by Brouwer.

    Behavioural Economics: Classical and Modern

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    In this paper, the origins and development of behavioural economics, beginning with the pioneering works of Herbert Simon (1953) and Ward Edwards (1954), is traced, described and (critically) discussed, in some detail. Two kinds of behavioural economics – classical and modern – are attributed, respectively, to the two pioneers. The mathematical foundations of classical behavioural economics is identified, largely, to be in the theory of computation and computational complexity; the corresponding mathematical basis for modern behavioural economics is, on the other hand, claimed to be a notion of subjective probability (at least at its origins in the works of Ward Edwards). The economic theories of behavior, challenging various aspects of 'orthodox' theory, were decisively influenced by these two mathematical underpinnings of the two theoriesClassical Behavioural Economics, Modern Behavioural Economics, Subjective Probability, Model of Computation, Computational Complexity. Subjective Expected Utility
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