Abstract
The theory of equilibrium and efficiency of resource allocation, initially developed for a world of certainty, has been reinterpreted for a world of uncertainty, thanks to a suggestion made by Arrow [1] and pursued further by Debreu [7].2
I am grateful to Mordecai Avriel, Freddy Delbaen, Louis Gevers, Roger Guesnerie and Dieter Sondermann for helpful comments and discussions. Earlier work on this subject with Dominique de la Vallée Poussin led to [11]. Support of the Fonds de la Recherche Fondamentale Collective, Brussels, under contract No. 611 is gratefully acknowledged.
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Notes
K. J. Arrow, ‘Le rôle des valeurs boursières pour la répartition la meilleure des risques’, pp. 41–7 in Econométrie Colloque International XL (Paris: CNRS, 1953); translated as ‘The Role of Securities in the Optimal Allocation of Risk-Bearing’, Review of Economic Studies, vol. XXXI (1964), pp. 91–6.
R. J. Aumann, ‘A Survey of Cooperative Games without Side Payments’, pp. 3–27 in Essays in Mathematical Economics edited by M. Shubik (Princeton: Princeton University Press, 1967).
M. Avriel, ‘Solution of Certain Non-Linear Programs Involving r-convex Functions’, Journal of Optimization Theory and Applications vol. XI (1973), pp. 159–74.
M. Avriel and A. C. Williams, ‘Complementary Convex Programming’, Mobil R. & D. Corporation, Progress Memorandum (May 1968).
E. Baudier, ‘L’introduction du temps dans la théorie de l’équilibre général’, Cahiers Economiques (1959), pp. 9–16.
K. Borch, ‘The Safety Loading of Reinsurance Premiums’, Skandinavisk Aktuarietidskrift vol. XLIII (1960), pp. 163–84.
G. Debreu, Theory of Value (New York: Wiley, 1959).
G. Debreu, ‘New Concepts and Techniques for Equilibrium Analysis’, International Economic Review vol. III (1962), pp. 257–73.
P. A. Diamond, ‘The Role of a Stock Market in a General Equilibrium Model with Technological Uncertainty’, American Economic Review vol. LVII (1967), pp. 759–76.
J. H. Drèze, ‘A Tâtonnement Process for Investment under Uncertainty in Private Ownership Economies’, pp. 3–23 in Mathematical Methods in Investment and Finance ed. by G. P. Szegö & K. Shell (Amsterdam: North-Holland, 1972).
J. H. Drèze and D. de la Vallée Poussin, ‘A Tâtonnement Process for Public Goods’, Review of Economic Studies vol. XXXVIII (1971), pp. 133–50.
E. Fama and M. H. Miller, The Theory of Finance (New York: Holt, Rinehart and Winston, 1972).
D. K. Foley, ‘Resource Allocation and the Public Sector’, Yale Economic Essays vol. VII (1967), pp. 45–98.
L. Gevers, ‘Competitive Equilibrium of the Stock Exchange and Pareto Efficiency’, chapter 10 infra.
J. M. Grandmont, ‘On the Short-Run Equilibrium in a Monetary Economy’, chapter 12 infra.
R. Guesnerie and T. de Montbrial, ‘Allocation under Uncertainty: a survey’, chapter 4 supra.
H. Konno, ‘Bilinear Programming: Part I: Algorithm for Solving Bilinear Programs; Part II: Application of Bilinear Programming’, (Stanford University, California, Technical Reports 9 and 10, 1971).
E. Malinvaud, Leçons de théorie microéconomique (Paris: Dunod, 1969).
E. Malinvaud, ‘Procédures pour la détermination d’un programme de consommations collectives’, mimeographed (Paris, 1969) (paper presented at the European Meeting of the Econometric Society, Brussels, 1969).
O. Mangasarian, Non-Linear Programming (New York: McGraw-Hill, 1969).
C. Milleron, ‘Theory of Value with Public Goods: A Survey Article’, Journal of Economic Theory vol. v (1972), pp. 419–77.
D. Sondermann, ‘Temporary Competitive Equilibrium under Uncertainty’, chapter 13 infra.
J. Stiglitz, ‘On the Optimality of the Stock Market Allocation of Investment’, The Quarterly Journal of Economics vol. LXXXVI (1972), pp. 25–60.
W. I. Zangwill, Non-Linear Programming, A Unified Approach (Englewood Cliffs: Prentice Hall, 1969).
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© 1974 International Economic Association
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Drèze, J.H. (1974). Investment Under Private Ownership: Optimality, Equilibrium and Stability. In: Drèze, J.H. (eds) Allocation under Uncertainty: Equilibrium and Optimality. International Economic Association Series. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-01989-2_9
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