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The Effects of Changes in Risk on Risk Taking: A Survey

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Handbook of Insurance

Abstract

We examine an important class of decision problems under uncertainty that entails the standard portfolio problem and the demand for coinsurance. The agent faces a controllable risk—his demand for a risky asset, for example—and a background risk. We determine how a change in the distribution in one of these two risks affects the optimal exposure to the controllable risk. Restrictions on first-order and second-order stochastic dominance orders are in general necessary to yield an unambiguous comparative statics property. We also review another line of research in which restrictions are made on preferences rather than on stochastic dominance orders.

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Notes

  1. 1.

    For more details, see Dionne et al. (1993) and more especially pages 315–317. See also Eeckhoudt-Gollier (1995) and more specifically page 183, Exercise 10.1. The reader who is interested in an insurance interpretation of some results in this survey may also refer to Alarie et al. (1992).

  2. 2.

    Gollier and Schlee (2006) examine the more general problem with a correlated background risk. More recent developments around these topics are also mentioned at the end of Sect. 5.6. Notice also that many results reviewed in this chapter also hold when final wealth is a concave function of α and \(\tilde{x}\).

  3. 3.

    For an excellent survey on stochastic dominance, see H. Levy (1992).

  4. 4.

    See Hardy et al. (1929).

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Acknowledgements

We thank two referees for their useful comments on a preliminary version of the chapter.

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Authors and Affiliations

  1. Iéseg School of Management (Lille) and CORE (Louvain), Lille, France

    Louis Eeckhoudt

  2. Toulouse School of Economics, University of Toulouse 1 Capitole, Toulouse, France

    Christian Gollier

Authors
  1. Louis Eeckhoudt
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  2. Christian Gollier
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Correspondence to Christian Gollier .

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Editors and Affiliations

  1. Finance, HEC Montreal, Montreal, Québec, Canada

    Georges Dionne

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Eeckhoudt, L., Gollier, C. (2013). The Effects of Changes in Risk on Risk Taking: A Survey. In: Dionne, G. (eds) Handbook of Insurance. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0155-1_5

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