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diff --git a/Master/texmf-dist/doc/plain/vertex/test.tex b/Master/texmf-dist/doc/plain/vertex/test.tex deleted file mode 100644 index f7e8514047e..00000000000 --- a/Master/texmf-dist/doc/plain/vertex/test.tex +++ /dev/null @@ -1,122 +0,0 @@ -\topmatter - -\title{Estimating Risk Aversion from \cr - Arrow-Debreu Portfolio Choice} - -\runningname{Hal R. Varian} -\runningtitle{Estimating Risk Aversion} - -\thanks{This research was supported in part by the National Science -Foundation. I would like to thank Richard Green for helpful remarks. I am -especially grateful to an anonymous referee whose comments significantly -improved the statements and proofs of the results.} - -\author{Hal R. Varian} - -\affil{University of Michigan} - -\date{October 27, 1984} - -\version{\today} - -\abstract{This paper derives necessary and sufficient conditions for -Arrow-Debreu choices of contingent consumption to be compatible with the -maximization of a state independent expected utility function that exhibits -increasing or decreasing absolute risk aversion, or increasing or -decreasing relative risk aversion. The conditions can be used to bound -different measures of risk aversion based on a single observation of -Arrow-Debreu portfolio choice.} - -\keywords{Revealed preference, expected utility, risk aversion, portfolio -choice.} - - -\address{Hal R. Varian, Department of Economics, University of Michigan, -Ann Arbor, MI 48109} - -\endtopmatter - -\document - -\noindent {\scten The expected utility} hypothesis forms the basis for much -of our understanding of investor behavior under uncertainty. It is -commonly agreed that a well-behaved expected utility function should be an -increasing and concave function of wealth, or, equivalently, that its first -derivative should be positive and its second derivative should be negative. -It is also widely accepted that the Arrow-Pratt measure of absolute risk -aversion should be declining with wealth. There is much less agreement -about the behavior of the Arrow-Pratt measure of {\it relative\/} risk -aversion, although some investigators have argued that it should increase -with wealth. - -In this note I derive necessary and sufficient conditions for choices of -contingent consumption across states of nature to satisfy various -hypotheses about the behavior of these measures of risk aversion. If the -portfolio choice behavior of the consumer is consistent with the conditions -I derive, then the conditions can be used to bound the Arrow--Pratt -measures of absolute and relative risk aversion. The conditions are -derived using methods of the ``nonparametric approach'' to optimizing -behavior introduced by Afriat (1967) and extended by Diewert (1973), -Diewert and Parkan (1978), and Varian (1982), (1983a). Applications of -these methods to choice under uncertainty include Dybvig and Ross (1982), -Green and Srivastava (1983), and Varian (1983b). - -\section The Maximization Problem - -Consider an investor who chooses a pattern of consumption across states of -nature to solve the following problem: - $$\max \sum_{s=1}^S \pi_s u(c_s) $$ - -\Refs - -\ref -\by{Afriat, S.} \yr{1967a} \paper{The Construction of a Utility -Function from Expenditure Data} \jour{International Economic Review} -\vol{8} \pages{67--77} -\endref - -\ref -\by{Afriat, S.} \yr{1967b} \paper{The Construction of Separable -Utility Functions from Expenditure Data} \paperinfo{mimeo, Purdue} -\endref - -\ref \by{Breeden, D. and R. Litzenberger} \yr{1978} \paper{Prices of -State-Contingent Claims Implicit in Option Prices} \jour{Journal of -Business} \pages{621--651} -\endref - -\ref -\by{Diewert, E.} \yr{1973} \paper{Afriat and Revealed Preference Theory} -\jour{Review of Economic Studies} \vol{40} \pages{419--426} -\endref - -\ref \by{Diewert, E. and C. Parkan} \yr{1978} \paper{Tests for Consistency -of Consumer Data and Nonparametric Index Numbers} \paperinfo{Working Paper -78-27, University of British Columbia} -\endref - -\ref \by{Dybvig, P. and S. Ross} \yr{1982} \paper{Portfolio Efficient Sets} -\jour{Econometrica} \pages{1525--1546} -\endref - -\ref \by{Green, R. and S. Srivastava} \yr{1983} \paper{Preference -Restrictions, Asset Returns, and Consumption} \paperinfo{mimeo, -Carnegie--Mellon University} -\endref - -\ref \by{Varian, H.} \yr{1982} \paper{The Nonparametric Approach to Demand -Analysis} \jour{Econometrica} \vol{50} \pages{945--973} -\endref - -\ref -\by{Varian, H.} \yr{1983a} \paper{Nonparametric Tests of Models of -Consumer Behavior} \jour{Review of Economic Studies} \vol{50} -\pages{99--110} -\endref - -\ref -\by{Varian, H.} \yr{1983b} \paper{Nonparametric Tests of Models of -Investor Behavior} \jour{Journal of Financial and Quantitative Analysis} -\vol{18} \pages{269--278} -\endref -
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