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Efficient and equilibrium allocations with stochastic differential utility. (English) Zbl 0804.90018
Summary: This paper presents results on the existence and characterization of Pareto efficient and of equilibrium allocations in a continuous-time setting under uncertainty in which agents have stochastic differential utility, a version of recursive utility. In order to characterize equilibrium and efficient allocations in terms of pointwise first-order conditions, uniform properness condition on preferences are avoided.

##### MSC:
 91B16 Utility theory 91B50 General equilibrium theory
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##### References:
 [1] Antonelli, F., Backward-forward stochastic differential equations, Annals of applied probability, 3, 777-793, (1991) · Zbl 0780.60058 [2] Araujo, A.; Monteiro, P., Equilibrium without uniform conditions, Journal of economic theory, 48, 416-427, (1989) · Zbl 0707.90017 [3] Arnold, V., Ordinary differential equations, (1992), Springer-Verlag New York [4] Dana, R.-A., Existence, uniqueness, and determinacy of Arrow-Debreu equilibria in finance models, (1991), Laboratoire de Mathématiques Fondamentales, University of Paris VI Paris, (Jussieu) [5] Dana, R.A.; LeVan, C., Structure of Pareto optima in an infinite-horizon economy where agents have recursive preferences, Journal of optimization theory and applications, 64, 269-292, (1990) · Zbl 0687.90020 [6] Dellacherie, C.; Mayer, P., Probabilities and potential B, (1982), North-Holland Amsterdam [7] Duffie, D., Stochastic equilibria: existence, spanning number and the ‘no expected financial gain from trade’ hypothesis, Econometrica, 54, 1161-1183, (1986) · Zbl 0602.90025 [8] Duffie, D.; Epstein, L., Stochastic differential utility, Econometrica, 60, 353-394, (1992) · Zbl 0763.90005 [9] Duffie, D.; Epstein, L., Asset pricing with stochastic differential utility, Review of financial studies, 5, 411-436, (1992) [10] Duffie, D.; Huang, C.-F., Implementing Arrow-Debreu equilibrium by continuous trading of few long-lived securities, Econometrica, 53, 1337-1356, (1985) · Zbl 0576.90014 [11] Duffie, D.; Lions, P.-L., PDE solutions of stochastic differential utility, Journal of mathematical economics, 21, 577-606, (1992) · Zbl 0768.90006 [12] Duffie, D.; Skiadas, C., Continuous-time security pricing: A utility gradient approach, Journal of mathematical economics, (1994), this issue · Zbl 0804.90017 [13] Duffie, D.; Zame, W., The consumption-based capital asset pricing model, Econometrica, 57, 1279-1297, (1989) · Zbl 0684.90007 [14] Ekeland, I.; Temam, R., Analyse convexe et problèmes variationels, (1974), Dunod Paris [15] Epstein, L., The global stability of efficient intertemporal allocations, Econometrica, 55, 329-355, (1987) · Zbl 0614.90022 [16] Geoffard, P.-Y., Utilité récursive: existence d’un chemin optimal de consommation, Comptes-rendus de l’académie des sciences, t. 312, Série I, 657-660, (1991) · Zbl 0714.90007 [17] Harrison, M.; Kreps, D., Martingales and arbitrage in multiperiod security markets, Journal of economic theory, 20, 381-408, (1979) · Zbl 0431.90019 [18] Holmes, R., Geometric functional analysis and its applications, (1975), Springer-Verlag New York · Zbl 0336.46001 [19] Kan, R., Structure of Pareto optima when agents have stochastic recursive preferences, Journal of economic theory, (1990), forthcoming · Zbl 0843.90021 [20] Karatzas, I.; Lehoczky, J.; Shreve, S., Equilibrium models with singular asset prices, Mathematical finance 1, 11-30, (1990), no. 3 [21] Karatzas, I.; Lehoczky, J.; Shreve, S., Existence and uniqueness of multi-agent equilibrium in a stochastic, dynamic consumption/investment model, Mathematics of operations research, 15, 80-128, (1990) · Zbl 0707.90018 [22] Koopmans, T., Stationary ordinal utility and impatience, Econometrica, 28, 287-309, (1960) · Zbl 0149.38401 [23] Lucas, R.; Stokey, N., Optimal growth with many consumers, Journal of economic theory, 32, 139-171, (1984) · Zbl 0525.90026 [24] Luenberger, D., Optimization by vector space methods, (1969), Wiley New York · Zbl 0176.12701 [25] Lucas, R.; Stokey, N., Optimal growth with many consumers, Journal of economic theory, 32, 139-171, (1984) · Zbl 0525.90026 [26] Mas-Colell, A., The theory of general equilibrium: A differentiable approach, (1985), Cambridge University Press Cambridge [27] Mas-Colell, A., The price equilibrium existence problem in topological vector lattices, Econometrica, 54, 1039-1054, (1986) · Zbl 0602.90028 [28] Mas-Colell, A.; Zame, W., Equilibrium in infinite-dimensional spaces, () · Zbl 0908.90036 [29] Pardoux, E.; Peng, S.-G., Adapted solutions of a backward stochastic differential equation, Systems and control letters, 14, 55-61, (1990) · Zbl 0692.93064 [30] Protter, P., Stochastic integration and differential equations, (1990), Springer-Verlag New York [31] Sundaresan, S., Intertemporally dependent preferences and the volatility of consumption and wealth, Review of financial studies, 2, 73-89, (1989) [32] Uzawa, H., Time preference, the consumption function, and optimum asset holdings, ()
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