Abstract
Probabilistic insurance is an insurance policy involving a small probability that the consumer will not be reimbursed. Survey data suggest that people dislike probabilistic insurance and demand more than a 20% reduction in the premium to compensate for a 1% default risk. While these preferences are intuitively appealing they are difficult to reconcile with expected utility theory. Under highly plausible assumptions about the utility function, willingness to pay for probabilistic insurance should be very close to willingness to pay for standard insurance less the default risk. However, the reluctance to buy probabilistic insurance is predicted by the weighting function of prospect theory. This finding highlights the potential role of the weighting function to explain insurance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Borch, K. (1974). “The Mathematical Theory of Insurance.” Lexington, MA: Lexington Books.
Camerer, C.F., and T.-H. Ho. (1994). “Violations of the Betweenness Axiom and Nonlinearity in Probability,” Journal of Risk and Uncertainty 8, 167–196.
Chew, S.H., and L.G. Epstein. (1989). “The Structure of Preferences and Attitudes towards the Timing of the Resolution of Uncertainty,” International Economic Review 30, 103–117.
Kahneman, D., and A. Tversky. (1979). “Prospect Theory: An Analysis of Decision under Risk,” Econometrica 47, 263–291.
Loomes, G., and R. Sugden. (1986). “Disappointment and Dynamic Consistency in Choice under Uncertainty,” Review of Economic Studies 53, 271–282.
Luce, R.D., and D. von Winterfeldt. (1994). “What Common Ground Exists for Descriptive, Prescriptive and Normative Utility Theories,” Management Science 40, 263–279.
Merton, R.L. (1971). “Optimum Consumption and Portfolio Rules in a Continuous-Time Model,” Journal of Economic Theory 3, 373–413.
Merton, R.C. (1993). “Operation and Regulation in Financial Intermediation: A Functional Perspective.” InP. Englund (Ed.), Operation and Regulation of Financial Markets, 17–68, The Economic Council, Stockholm.
Mossin, J. (1968). “Aspects of Rational Insurance Purchasing,” Journal of Political Economy 76, 553–568.
Prelec, D. (1995). “The Probability Weighting Function,” Econometrica, forthcoming.
Quiggin, J. (1981). “Risk Perception and Risk Aversion among Australian Farmers,” Australian Journal of Agricultural Economics 25, 160–169.
Schmeidler, D. (1989). “Subjective Probability and Expected Utility without Additivity,” Econometrica 57, 571–587.
Segal, U. (1988). “Probabilistic Insurance and Anticipated Utility,” Journal of Risk and Insurance 55, 287–297.
Segal, U. (1990). “Two-Stage Lotteries without the Reduction Axiom,” Econometrica 58, 349–377.
Segal, U., and A. Spivak (1990). “First-Order versus Second-Order Risk-Aversion,” Journal of Economic Theory 51, 111–125.
Tversky, A., and D. Kahneman (1992). “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Risk and Uncertainty 5, 297–323.
Tversky, A., and P.P. Wakker (1995). “Risk Attitudes and Decision Weights,” Econometrica 63, 1255–1280.
Viscusi, W.K. (1995). “Government Action, Biases in Risk Perception, and Insurance Decisions,” Geneva Papers in Risk and Insurance Theory 20, 93–110.
Wu, G., and R. Gonzalez (1996). “Curvature of the Probability Weighting Function,” Management Science 42, 1676–1690.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
WAKKER, P., THALER, R. & TVERSKY, A. Probabilistic Insurance. Journal of Risk and Uncertainty 15, 7–28 (1997). https://doi.org/10.1023/A:1007799303256
Issue Date:
DOI: https://doi.org/10.1023/A:1007799303256