Abstract
This paper investigates further the connection between the concept of risk-aversion and the property of concavity of the utility function of the agent. Improved specifications of the Jensen inequality are used for stating a number of local properties of certainty equivalents under milder regularity assumptions on the utility function than those made in literature. The paper concludes by illustrating a few applications of this theory.
Riassunto
Si approfondisce lo studio del legame tra il concetto di avversione al rischio e quello di concavità della funzione di utilità dell'agente. Nel lavoro vengono utilizzate estesamente versioni migliorate della disuguaglianza di Jensen che consentono di fornire alcuni risultati locali sotto ipotesi deboli di regolarità sulla funzione di utilità. Il lavoro termina fornendo alcune applicazioni di questa analisi nell'ambito della teoria delle scelte in ambito rischioso.
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References
Arrow K. J.,Aspects of a Theory of Risk Bearing, Yrjo Jahnsson Lectures, Helsinki, 1965. Reprinted inEssay in the Theory of Risk Bearing, Markham Publishing Co., Chicago, 1971.
deFinetti B.,Sulla preferibilità, Giornale degli Economisti e Annali di Economia, 1952, 685–709.
La Valle I. A.,On Cash Equivalents and Information Evaluation in Decisions Under Uncertainty — Part I: Basic Theory, Journal of the American Statistical Association,36, 1968, 252–276.
Montrucchio L.,Lipschitz Continuous Policy Functions for Strongly Concave Optimization Problems, Journal of Mathematical Economics,16, 1987, 259–273.
Montrucchio L.,Dynamic Complexity of Optimal Paths and Discout Factors for Strongly Concave Problems, Journal of Optimization Theory and Applications, 1994, forthcoming.
Montrucchio L., Peccati L.,A Note on Shiu-Fisher-Weil Immunization Theorem, Insurance: Mathematics and Economics,10, 1991, 125–131.
Montrucchio L., Tibiletti L.,Sulla misura di avversione al rischio di de-Finetti-Arrow-Pratt, Atti del XVII Convegnoamases, Ischia, 8–11 settembre, 1993, 655–674.
Penot J. P., Volle M.,On Strongly Convex and Paraconvex Dualities, Generalized Convexity and Fractional Programming with Economic Applications, Edited by A. Cambini, E. Castagnoli, L. Martein, P. Mazzoleni, and S. Schaible, Springer-Verlag, Berlin, Germany, 1990, 198–218.
Pratt J. W.,Risk aversion in the small and in the large, Econometria,32, 1964, 122–136.
Rockafeller T. R.,Saddle Points of Hamiltonianan Systems in Convex Lagrange Problems Having a Nonzero Discount Rate, Journal of Economic Theory,12, 1976, 71–113.
Samuelson P. A.,Risk and uncertainty: A fallacy of large numbers, Scientia, 6th series,57, 1963, 1–6.
Schaible S., Ziemba W. T., Editors,Generalized Concavity in Optimization and Economics, Academic Press, New York, 1981.
Segal U., Spivak A.,First Order versus Second Order Risk Aversion, Journal of Economic Theory,51, 1990, 11–125.
Vial J. P.:Strong and Weak Convexity of Sets and Functions, Mathematics of Operation Research,8, 1983, 231–259.
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This research was partially supported by M.U.R.S.T. “Dinamiche Non-Lineari e Applicazioni alle Scienze Economiche e Sociali”.
Although the paper is co-authoured, we specify that Sections 3 and 4 are to be attributed to Luigi Montrucchio, while Sections 1, 2 and 5 to Luisa Tibiletti.
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Montrucchio, L., Tibiletti, L. Risk aversion in the small and Jensen inequalities. Rivista di Matematica per le Scienze Economiche e Sociali 16, 21–37 (1993). https://doi.org/10.1007/BF02095123
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DOI: https://doi.org/10.1007/BF02095123