How risky is a random process? |
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| Institution: | 1. Center for Mathematical Economics, Bielefeld University, Germany;2. Faculty of Economic and Financial Sciences, University of Johannesburg, South Africa;1. Department of Mathematics, University of Bayreuth, Germany;2. Department of Economics, University of Bayreuth, Germany;3. Public Choice Research Centre, University of Turku, Finland;1. LAMETA – INRA – CNRS – SupAgro-Univ. Montpellier, 2 place Viala, 34060 Montpellier, France;2. IESEG School of Management – LEM – CNRS, 3 rue de la Digue, 59000 Lille, France;3. CIRED–CNRS–EHESS–Ecole des Ponts ParisTech, 45 bis avenue de la Belle-Gabrielle, 94736 Nogent Sur Marne Cedex, France |
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| Abstract: | The riskiness of random processes is compared by (a) employing a decision theoretic equivalence between processes and lotteries on path-spaces to identify the riskiness of the former with that of the latter, and (b) using the theory of comparative riskiness of lotteries over vector spaces to compare the riskiness of lotteries on a given path-space. We derive the equivalence used in step (a) and contribute a new criterion to the theory applied in step (b). The validity of the new criterion, which applies second order stochastic dominance to utility distributions, is established by showing its equivalence to the benchmark decision theoretic criterion when comparing the riskiness of lotteries over any vector space. We demonstrate the theory’s tractability via diverse economic applications. |
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| Keywords: | Random processes Vector outcomes Comparative riskiness Utility-based second order stochastic dominance Monotone comparative statics |
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