Risk Transformations, Deductibles, and Policy Limits

Rothschild and Stiglitz (1970, 1971) pioneered the study of how an increase in risk affects the demand for a risky asset. Gollier (1995) first identified a necessary and sufficient condition for unambiguous comparative statics for demand under transformations of the asset's probability distribu...

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Bibliographic Details
Published in:The Journal of risk and insurance 2001-09, Vol.68 (3), p.465-473
Main Authors: Powers, Michael R., Tzeng, Larry Y.
Format: Article
Language:English
Subjects:
Assets
Deductible coverage
deductibles
Demand
Economic theory
Insurance
Insurance coverage
Insurance deductibles
Insurance industry
Insurance policies
Insurance regulation
Insurance settlements
Liability insurance
Management
Mathematical models
Mathematical transformations
Methods
optimization
Prices and rates
Probability distribution
Risk
Risk aversion
Risk management
Self insurance
Studies
Sufficient conditions
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Summary:Rothschild and Stiglitz (1970, 1971) pioneered the study of how an increase in risk affects the demand for a risky asset. Gollier (1995) first identified a necessary and sufficient condition for unambiguous comparative statics for demand under transformations of the asset's probability distribution function. In this article, the authors examine the necessary and sufficient conditions for unambiguous comparative statics for insurance demand for coverage deductibles and policy limits, when the loss variable undergoes certain classes of transformations. The authors show that, if a transformation is both mean-preserving above (below) the optimal deductible (policy limit), and probability-preserving above (below) the optimal deductible (policy limit), then the necessary and sufficient condition is given by first-order stochastic dominance below (above) the optimal point.
ISSN:0022-4367
1539-6975
DOI:10.2307/2678119