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

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 withou...

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Bibliographic Details
Published in:The American economic review 2004-09, Vol.94 (4), p.1130-1140
Main Author: Somerville, R. A.
Format: Article
Language:English
Subjects:
Casualty insurance
Consumption
Demand
Economic theory
Health insurance
Insurance
Insurance premiums
Insurance rates
Life insurance
Maximum principle
Risk aversion
Risk premiums
Savings
Studies
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Summary: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.
ISSN:0002-8282
1944-7981
DOI:10.1257/0002828042002642