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Efficient Intertemporal Allocations with Recursive Utility

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  • Bernard Dumas
  • Raman Uppal
  • Tan Wang

Abstract

In this article, our objective is to determine efficient allocations in economies with multiple agents having recursive utility functions. Our main result is to show that in a multiagent economy, the problem of determining efficient allocations can be characterized in terms of a single value function (that of a social planner), rather than multiple functions (one for each investor), as has been proposed thus far (Duffie, Geoffard and Skiadas (1994)). We then show how the single value function can be identified using the familiar technique of stochastic dynamic programming. We achieve these goals by first extending to a stochastic environment Geoffard's (1996) concept of variational utility and his result that variational utility is equivalent to recursive utility, and then using these results to characterize allocations in a multiagent setting.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0231.

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Date of creation: Apr 1998
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Publication status: published as Dumas, Bernard, Raman Uppal and Tan Wang. "Efficient Intertemporal Allocations With Recursive Utility," Journal of Economic Theory, 2000, v93(2,Aug), 240-259.
Handle: RePEc:nbr:nberte:0231

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  1. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
  2. Svensson, L.E.O., 1988. "Portfolio Choice With Non-Expected Utility In Continuous Time," Papers, Stockholm - International Economic Studies 423, Stockholm - International Economic Studies.
  3. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, Econometric Society, vol. 57(4), pages 937-69, July.
  4. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, Econometric Society, vol. 54(5), pages 1039-53, September.
  5. David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
  6. Kan Rui, 1995. "Structure of Pareto Optima When Agents Have Stochastic Recursive Preferences," Journal of Economic Theory, Elsevier, Elsevier, vol. 66(2), pages 626-631, August.
  7. Geoffard, Pierre-Yves, 1996. "Discounting and Optimizing: Capital Accumulation Problems as Variational Minmax Problems," Journal of Economic Theory, Elsevier, Elsevier, vol. 69(1), pages 53-70, April.
  8. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(1), pages 1-71.
  9. Costis Skiadas, 1998. "Recursive utility and preferences for information," Economic Theory, Springer, Springer, vol. 12(2), pages 293-312.
  10. Dumas, Bernard, 1989. "Two-Person Dynamic Equilibrium in the Capital Market," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 2(2), pages 157-88.
  11. Epstein, Larry G, 1987. "The Global Stability of Efficient Intertemporal Allocations," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 329-55, March.
  12. Weil, Philippe, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 105(1), pages 29-42, February.
  13. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 81, Cowles Foundation for Research in Economics, Yale University.
  14. Constantinides, George M, 1982. "Intertemporal Asset Pricing with Heterogeneous Consumers and without Demand Aggregation," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 55(2), pages 253-67, April.
  15. Lucas, Robert Jr. & Stokey, Nancy L., 1984. "Optimal growth with many consumers," Journal of Economic Theory, Elsevier, Elsevier, vol. 32(1), pages 139-171, February.
  16. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-36.
  17. Duffie, Darrell & Geoffard, Pierre-Yves & Skiadas, Costis, 1994. "Efficient and equilibrium allocations with stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 133-146, March.
  18. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, Econometric Society, vol. 60(2), pages 353-94, March.
  19. Dana, Rose-Anne & Van, Cuong Le, 1991. "Optimal growth and Pareto optimality," Journal of Mathematical Economics, Elsevier, vol. 20(2), pages 155-180.
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Citations

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Cited by:
  1. Bernard Dumas & Pascal Maenhout, 2002. "A Central-Planning Approach to Dynamic Incomplete-Market Equilibrium," Levine's Working Paper Archive 391749000000000523, David K. Levine.
  2. Roche, Hervé, 2011. "Asset prices in an exchange economy when agents have heterogeneous homothetic recursive preferences and no risk free bond is available," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 35(1), pages 80-96, January.
  3. Peter Klibanoff & Emre Ozdenoren, 2007. "Subjective recursive expected utility," Economic Theory, Springer, Springer, vol. 30(1), pages 49-87, January.
  4. Felix KUBLER & Karl SCHMEDDERS, . "Non-parametric counterfactual analysis in dynamic general equilibrium," Swiss Finance Institute Research Paper Series, Swiss Finance Institute 09-05, Swiss Finance Institute.
  5. Hansen, Lars Peter & Sargent, Thomas J., 2012. "Three types of ambiguity," Journal of Monetary Economics, Elsevier, Elsevier, vol. 59(5), pages 422-445.
  6. Roche, Herve, 2003. "Stochastic growth: a duality approach," Journal of Economic Theory, Elsevier, Elsevier, vol. 113(1), pages 131-143, November.
  7. Larry G. Epstein & JianJun Miao, 2001. "A Two-Person Dynamic Equilibrium under Ambiguity," RCER Working Papers 478, University of Rochester - Center for Economic Research (RCER).
  8. Karen K. Lewis, 2011. "Global asset pricing," Globalization and Monetary Policy Institute Working Paper, Federal Reserve Bank of Dallas 88, Federal Reserve Bank of Dallas.
  9. Buss, Adrian & Uppal, Raman & Vilkov, Grigory, 2014. "Asset prices in general equilibrium with recursive utility and illiquidity induced by transactions costs," SAFE Working Paper Series 41, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
  10. Isaenko, Sergei, 2008. "The term structure of interest rates in a pure exchange economy where investors have heterogeneous recursive preferences," The Quarterly Review of Economics and Finance, Elsevier, Elsevier, vol. 48(3), pages 457-481, August.
  11. Dumas, Bernard & Harvey, Campbell R. & Ruiz, Pierre, 2000. "Are Correlations of Stock Returns Justified by Subsequent Changes in National Outputs?," Working Papers, University of Pennsylvania, Wharton School, Weiss Center 00-2, University of Pennsylvania, Wharton School, Weiss Center.
  12. Anderson, Evan W., 2005. "The dynamics of risk-sensitive allocations," Journal of Economic Theory, Elsevier, Elsevier, vol. 125(2), pages 93-150, December.

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