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Insurance, Consumption, and Saving: A Dynamic Analysis in Continuous Time

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  • R.A. Somerville

Abstract

This paper shows how the demand for non-life insurance interacts with consumption and saving. The analysis is set in continuous time, using the maximum principle. When insurance is actuarially fair, the insurance and consumption decisions are separable. With loaded premiums, and alternatively without insurance, optimal consumption is dynamically related to the growth rate of the loss probability, and a growing loss probability generates precautionary saving. With loaded premiums, less than full insurance is demanded at each instant, and optimal cover varies over time, whether or not the loss probability is constant.

Suggested Citation

  • R.A. Somerville, 2004. "Insurance, Consumption, and Saving: A Dynamic Analysis in Continuous Time," American Economic Review, American Economic Association, vol. 94(4), pages 1130-1140, September.
  • Handle: RePEc:aea:aecrev:v:94:y:2004:i:4:p:1130-1140
    Note: DOI: 10.1257/0002828042002642
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    References listed on IDEAS

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    1. Olivia S. Mitchell, 1999. "New Evidence on the Money's Worth of Individual Annuities," American Economic Review, American Economic Association, vol. 89(5), pages 1299-1318, December.
    2. Cooper, Russell & Hayes, Beth, 1987. "Multi-period insurance contracts," International Journal of Industrial Organization, Elsevier, vol. 5(2), pages 211-231.
    3. Dionne, Georges & Eeckhoudt, Louis, 1984. "Insurance and saving: some further results," Insurance: Mathematics and Economics, Elsevier, vol. 3(2), pages 101-110, April.
    4. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, Oxford University Press, vol. 90(4), pages 629-649.
    5. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December.
    6. David F. Bradford & Kyle Logue, 1998. "The Effects of Tax Law Changes on Property-Casualty Insurance Prices," NBER Chapters,in: The Economics of Property-Casualty Insurance, pages 29-80 National Bureau of Economic Research, Inc.
    7. Mayers, David & Smith, Clifford W, Jr, 1983. "The Interdependence of Individual Portfolio Decisions and the Demand for Insurance," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 304-311, April.
    8. Eeckhoudt, Louis & Meyer, Jack & Ormiston, Michael B, 1997. "The Interaction between the Demands for Insurance and Insurable Assets," Journal of Risk and Uncertainty, Springer, vol. 14(1), pages 25-39, January.
    9. Joseph G. Eisenhauer, 2002. "Relative Effects of Premium Loading and Tax Deductions on the Demand for Insurance," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 25(1), pages 47-62.
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    Cited by:

    1. repec:spo:wpecon:info:hdl:2441/4422 is not listed on IDEAS
    2. Frédéric Gannon & Vincent Touzé, 2006. "Insurance and Optimal Growth," Post-Print halshs-00085181, HAL.

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