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The Economics of Adding and Subdividing Independent Risks: Some Comparative Statics Results

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  • Eeckhoudt, Louis
  • Gollier, Christian
  • Levasseur, Michel

Abstract

In this paper we address the problem of determining whether adding independent risks or subdividing them is a good substitute for insurance. Despite the fact that accepting more i.i.d. risks increases total risk, it is shown that some risk-averse decision makers can rationally reduce their demand for insurance by doing so. Similarly, a better diversified portfolio of i.i.d. risky assets can rationally be more insured, even if diversification is a risk-reduction scheme. We derive conditions sufficient to obtain unambiguous comparative statics results. Assuming that absolute risk aversion is decreasing and that the fourth derivative of the utility function is positive, we show that diversification is an exceptionally good substitute for insurance. Under the same conditions, adding independent risks to wealth reduces the demand for insurance on each unit. Copyright 1993 by Kluwer Academic Publishers

Suggested Citation

  • Eeckhoudt, Louis & Gollier, Christian & Levasseur, Michel, 1993. "The Economics of Adding and Subdividing Independent Risks: Some Comparative Statics Results," Journal of Risk and Uncertainty, Springer, vol. 7(3), pages 325-337, December.
    • Handle: RePEc:kap:jrisku:v:7:y:1993:i:3:p:325-37
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    Cited by:

    1. Gollier, Christian & Lindsey, John & Zeckhauser, Richard J., 1997. "Investment Flexibility and the Acceptance of Risk," Journal of Economic Theory, Elsevier, vol. 76(2), pages 219-241, October.
    2. Gollier, Christian, 1994. "Dynamic Risk Taking With Indivisible Risks," Working Papers 013, Risk and Insurance Archive.
    3. Gollier, Christian, 1994. "Second-Best Risk Sharing With Incomplete Contracts," Working Papers 015, Risk and Insurance Archive.
    4. Lajeri-Chaherli, Fatma, 2004. "Proper prudence, standard prudence and precautionary vulnerability," Economics Letters, Elsevier, vol. 82(1), pages 29-34, January.
    5. Markus Huggenberger & Peter Albrecht, 2022. "Risk pooling and solvency regulation: A policyholder's perspective," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 89(4), pages 907-950, December.
    6. Gollier, Christian, 1996. "Decreasing absolute prudence: Characterization and applications to second-best risk sharing," European Economic Review, Elsevier, vol. 40(9), pages 1799-1815, December.

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