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Optimal Reference Points and Anticipation

  • Todd Sarver

This paper considers a model of reference-dependent utility in which the individual makes a conscious choice of her reference point for future consumption. The model incorporates the combination of loss aversion and anticipatory utility as competing forces in the determination of the optimal reference point: anticipating better outcomes boosts current utility but also raises the reference level for future consumption, making the individual more susceptible to losses. A central focus of the paper is on the implications of this model of Optimal Anticipation for attitudes toward risk in dynamic environments. The main representation is formulated in an infinite-horizon framework, and axiomatic foundations are provided. I also describe special cases and show in particular that recursive expected utility in the sense of Epstein and Zin (1989) and Kreps and Porteus (1978) can be reinterpreted in terms of optimal anticipation and loss aversion. Finally, I describe a homogeneous version of the model and apply it to a portfolio choice problem. I show that asset pricing for the Optimal Anticipation model is based on simple modifications of standard Euler equations. While maintaining tractability, this model is rich enough to permit first-order risk aversion and can overcome several deficits of standard expected utility, such as the equity premium puzzle and Rabin's paradox. JEL Classification: D03, D81, G12

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1566.

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Date of creation: 18 Jun 2012
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Handle: RePEc:nwu:cmsems:1566
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  1. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of Security Market Data for Models of Dynamic Economies," NBER Technical Working Papers 0089, National Bureau of Economic Research, Inc.
  2. Phillippe Weil, 1997. "The Equity Premium Puzzle and the Risk-Free Rate Puzzle," Levine's Working Paper Archive 1833, David K. Levine.
  3. Sarver, Todd & Ergin, Haluk, 2015. "Hidden actions and preferences for timing of resolution of uncertainty," Theoretical Economics, Econometric Society, vol. 10(2), May.
  4. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
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  7. L. Epstein & S. Zin, 2010. "First order risk aversion and the equity premium puzzle," Levine's Working Paper Archive 1400, David K. Levine.
  8. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  9. TallariniJr., Thomas D., 2000. "Risk-sensitive real business cycles," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 507-532, June.
  10. Epstein, Larry G. & Zin, Stanley E., 2001. "The independence axiom and asset returns," Journal of Empirical Finance, Elsevier, vol. 8(5), pages 537-572, December.
  11. Marinacci, Massimo & Montrucchio, Luigi, 2010. "Unique solutions for stochastic recursive utilities," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1776-1804, September.
  12. Bekaert, G.R.J. & Hodrick, R. & Marshall, D., 1997. "The implications of first-order risk aversion for asset market risk premiums," Discussion Paper 1997-07, Tilburg University, Center for Economic Research.
  13. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
  14. Nicholas Barberis & Ming Huang & Tano Santos, 1999. "Prospect Theory and Asset Prices," NBER Working Papers 7220, National Bureau of Economic Research, Inc.
  15. Weil, Philippe, 1990. "Nonexpected Utility in Macroeconomics," The Quarterly Journal of Economics, MIT Press, vol. 105(1), pages 29-42, February.
  16. 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, vol. 57(4), pages 937-69, July.
  17. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-92, July.
  18. Faruk Gul & Wolfgang Pesendorfer, 2004. "Self-Control and the Theory of Consumption," Econometrica, Econometric Society, vol. 72(1), pages 119-158, 01.
  19. Caplin, Andrew & Leahy, John, 1997. "Psychological Expected Utility Theory and Anticipatory Feelings," Working Papers 97-37, C.V. Starr Center for Applied Economics, New York University.
  20. Barillas, Francisco & Hansen, Lars Peter & Sargent, Thomas J., 2009. "Doubts or variability?," Journal of Economic Theory, Elsevier, vol. 144(6), pages 2388-2418, November.
  21. Sanford J. Grossman & Guy Laroque, 1987. "Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods," NBER Working Papers 2369, National Bureau of Economic Research, Inc.
  22. Narayana R. Kocherlakota, 1996. "The Equity Premium: It's Still a Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(1), pages 42-71, March.
  23. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151.
  24. Benartzi, Shlomo & Thaler, Richard H, 1995. "Myopic Loss Aversion and the Equity Premium Puzzle," The Quarterly Journal of Economics, MIT Press, vol. 110(1), pages 73-92, February.
  25. Kreps, David M. & Porteus, Evan L., 1979. "Temporal von neumann-morgenstern and induced preferences," Journal of Economic Theory, Elsevier, vol. 20(1), pages 81-109, February.
  26. Xavier Gabaix & David Laibson, 2002. "The 6D Bias and the Equity Premium Puzzle," Harvard Institute of Economic Research Working Papers 1947, Harvard - Institute of Economic Research.
  27. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
  28. Larry G. Epstein, 2008. "Living with Risk," Review of Economic Studies, Oxford University Press, vol. 75(4), pages 1121-1141.
  29. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
  30. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
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