Real indeterminacy with financial assets
The purpose of this paper, which takes up after D. Cass (1984a, 1984b) is to find the degree of real indeterminacy inherent in models with purely financial assets. We solve the problem for the case where there are enough traders (precisely, the number of traders is larger than the number of bonds) and the asset returns structure is in general position. We find that if the number of bonds is non-zero and fewer than the number of states then, generically, the number of dimensions of real indeterminacy is S-1, one less than the number of states. There is something of a surprise in the above result, namely the dimension of real indeterminacy does not depend on the number of bonds (except in the two limit cases). Indeed one initial conjecture was S-B. This points to an intriguing qualitative discontinuity at the complete market configuration. If markets are financially complete then the model is determinate. Let just one bond be missing and the model become highly indeterminate. Thus, in this sense, the complete markets hypothesis lacks robustness.
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- David Cass, 2006.
"Competitive Equilibrium with Incomplete Financial Markets,"
PIER Working Paper Archive
06-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Cass, David, 2006. "Competitive equilibrium with incomplete financial markets," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 384-405, August.
- Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
- Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
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