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Market behavior when preferences are generated by second-order stochastic dominance

  • Dana, Rose-Anne

We develop a theory of decision making and General Equilibrium for contingent markets when incomplete preferences are generated by second-order stochastic dominance (SSD). Demand, Pareto-optima and equilibria dominance are fully characterized. Demands and equilibrium allocations are non-increasing functions of the pricing density and Pareto-optimal allocations are comonotone. They generalize mean–variance demands and CAPM equilibrium allocations which are non-increasing affine functions of the pricing density. They are not observationally distinguishable from those of von-Neumann–Morgenstern decision makers with increasing strictly concave utilities nor from those of strict risk averse non-expected utility maximizers. We also show that expenditure functions associated to second-order stochastic dominance, provide microeconomic foundations for a class of law invariant risk-measures used in mathematical finance.

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Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/6697.

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Date of creation: 2004
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Publication status: Published in Journal of Mathematical Economics, 2004, Vol. 40, no. 6. pp. 619-639.Length: 20 pages
Handle: RePEc:dau:papers:123456789/6697
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  1. Chateauneuf, A. & Cohen, M. & Meilijson, I., 1997. "New Tools to Better Model Behavior Under Risk and UNcertainty: An Oevrview," Papiers d'Economie Mathématique et Applications 97.55, Université Panthéon-Sorbonne (Paris 1).
  2. Peleg, Bezalel & Yaari, M E, 1975. "A Price Characterization of Efficient Random Variables," Econometrica, Econometric Society, vol. 43(2), pages 283-92, March.
  3. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  4. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-93, July.
  5. Gollier, Christian & Schlesinger, Harris, 1996. "Arrow's Theorem on the Optimality of Deductibles: A Stochastic Dominance Approach," Economic Theory, Springer, vol. 7(2), pages 359-63, February.
  6. Kim, Chongmin, 1998. "Stochastic Dominance, Pareto Optimality, and Equilibrium Asset Pricing," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 341-56, April.
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