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A Model of Comparative Statics for Changes in Stochastic Returns with Dependent Risky Assets

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  • Dionne, Georges
  • Gollier, Christian

Abstract

In this article, we show how the order of Linear Stochastic Dominance proposed by Gollier (1995) can be applied to situations with dependent risky assets. This order was shown to be the least constrained necessary and sufficient condition to guarantee that all risk-averse agents reduce their risky position when an increase in risk is imposed. This was done in a model with only one source of risk, as in the standard portfolio problem with one safe asset and one risky asset. We obtain the necessary and sufficient condition for a change in the joint distribution of returns to yield an unambiguous comparative statics result when the two assets are risky. We show in particular that the concept of Linear Stochastic Dominance is sufficient to generate the desired result. These results are linked to existing sufficient conditions in the one-safe-one-risky-asset model, as the condition of strong increase in risk or the monotone likelihood ratio order. They are also compared to those in models where restrictions are on the set of concave utility functions. Copyright 1996 by Kluwer Academic Publishers

Suggested Citation

  • Dionne, Georges & Gollier, Christian, 1996. "A Model of Comparative Statics for Changes in Stochastic Returns with Dependent Risky Assets," Journal of Risk and Uncertainty, Springer, vol. 13(2), pages 147-162, September.
    • Handle: RePEc:kap:jrisku:v:13:y:1996:i:2:p:147-62
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    Cited by:

    1. Anissa Chaibi & Maria-Lenuta Ciupac-Ulici & Mircea-Cristian Gherman, 2014. "Do Recent Stochastic Tools Help to Better Understand Investors Preference and Asset Allocation?," Working Papers 2014-130, Department of Research, Ipag Business School.
    2. Inmaculada Rodríguez-Puerta & Alberto A. Álvarez-López, 2022. "A model for the optimal selection of lenders," Annals of Operations Research, Springer, vol. 313(2), pages 1269-1284, June.
    3. Burton Hollifield & Alan Kraus, 2009. "Defining Bad News: Changes in Return Distributions That Decrease Risky Asset Demand," Management Science, INFORMS, vol. 55(7), pages 1227-1236, July.
    4. Amigues, Jean-Pierre & Favard, Pascal & Gaudet, Gerard & Moreaux, Michel, 1998. "On the Optimal Order of Natural Resource Use When the Capacity of the Inexhaustible Substitute Is Limited," Journal of Economic Theory, Elsevier, vol. 80(1), pages 153-170, May.
    5. Choi, Gyemyung & Kim, Iltae & Snow, Arthur, 2000. "Comparative statics predictions for the cross-effects of central dominance changes in risk with quasilinear payoffs," Economics Letters, Elsevier, vol. 66(1), pages 41-48, January.
    6. Dachraoui, Kais & Dionne, Georges, 2001. "Stochastic dominance and optimal portfolio," Economics Letters, Elsevier, vol. 71(3), pages 347-354, June.
    7. Gollier Christian & Schlee Edward E, 2006. "Increased Risk-Bearing with Background Risk," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-29, March.

    More about this item

    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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