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Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with a riskless asset

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Date
1999
Dewey
Economie financière
Sujet
Equilibrium; Risk aversion; Economy
JEL code
D51
Journal issue
Journal of Mathematical Economics
Volume
32
Number
2
Publication date
1999
Article pages
167-175
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/S0304-4068(98)00050-0
URI
https://basepub.dauphine.fr/handle/123456789/6112
Collections
  • CEREMADE : Publications
Metadata
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Author
Dana, Rose-Anne
Type
Article accepté pour publication ou publié
Abstract (EN)
In this note, we study the problem of existence, uniqueness and determinacy of equilibrium in the two period mean-variance C.A.P.M. with a riskless asset and possibly an infinite number of assets. The existence, uniqueness and determinacy problem is brought down to a two-dimensional problem. We construct a reduced two-dimensional economy which has the same equilibria as the original economy. In particular, we provide a very elementary proof of existence of equilibrium. We then show that when utilities are additively separable in mean and variance, sufficient conditions for uniqueness of equilibrium may be given in terms of ‘risk aversion'. Lastly, we show that generically equilibria are determinate.

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