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Portfolio Dominance, Lower Conditional Expectation And The Monotone Likelihood Ratio Order

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  • Gollier, Christian

Abstract

In the standard portfolio problem, a shift in the distribution of the risky asset is ``portfolio-dominated'' if it reduces the demand for the risky asset by all risk-averse agents, whatever the riskfree rate. We show that the condition obtained by Landsberger and Meilijson [1993] (while necessary) is not sufficient for portfolio dominance and we present the exact necessary and sufficient condition for portfolio dominance. It is shown that, if the comparative statics property holds for any concave utility functions that are piecewise linear with two kinks, it also holds for the set of all concave utility functions. Portfolio dominance is stronger than second-degree stochastic dominance, but weaker than the monotone likelihood ratio order. We also show that the monotone likelihood ratio order is necessary and sufficient to yield the same unambiguous comparative statics property for a larger class of (nonlinear) payoff functions.

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Bibliographic Info

Paper provided by Risk and Insurance Archive in its series Working Papers with number 014.

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Date of creation: Aug 1993
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Handle: RePEc:wop:riskar:014

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Related research

Keywords: portfolio problem; demand for insurance; central riskiness.;

References

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  1. Ormiston Michael B. & Schlee Edward E., 1993. "Comparative Statics under Uncertainty for a Class of Economic Agents," Journal of Economic Theory, Elsevier, vol. 61(2), pages 412-422, December.
  2. Meyer, Jack & Ormiston, Michael B., 1983. "The comparative statics of cumulative distribution function changes for the class of risk averse agents," Journal of Economic Theory, Elsevier, vol. 31(1), pages 153-169, October.
  3. Meyer, Jack & Ormiston, Michael B, 1985. "Strong Increases in Risk and Their Comparative Statics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 425-37, June.
  4. Miles S. Kimball, 1991. "Standard Risk Aversion," NBER Technical Working Papers 0099, National Bureau of Economic Research, Inc.
  5. Dionne, Georges & Eeckhoudt, Louis & Gollier, Christian, 1993. "Increases in Risk and Linear Payoffs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(2), pages 309-19, May.
  6. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
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Cited by:
  1. Machnes, Yaffa, 1995. "Deductible insurance and production," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 119-123, October.

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