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Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory

Author

Listed:
  • Wing Yan Lee

    (Department of Mathematics, Statistics and Insurance, The Hang Seng University of Hong Kong, Hang Shin Link, Shatin, Hong Kong, China)

  • Derrick W. H. Fung

    (Department of Mathematics, Statistics and Insurance, The Hang Seng University of Hong Kong, Hang Shin Link, Shatin, Hong Kong, China)

Abstract

People take different measures to control risks. The measures that can simultaneously reduce loss probability and loss size are called self-insurance-cum-protection. This paper studies self-insurance-cum-protection using Yaari’s dual theory. We analyze the comparative statics of increased risk aversion. Two different sufficient conditions are found in the two-state model, from which an increase in the level of risk aversion will lead to an increase in the level of self-insurance-cum-protection. The first condition is a new result under Yaari’s dual theory and its implication is that the more risk-averse individual is willing to exert greater effort on self-insurance-cum-protection if the probability of loss can be reduced to very small by a less risk-averse individual with optimal effort. The second condition depends on the forms of the self-insurance-cum protection cost and the loss. This condition is the same as that obtained under expected utility in existing literature. Our study therefore assures the robustness this result. We also study comparative statics in the continuous model and find out that the results are analogous to that in the two-state model. In addition, we consider how the availability of market insurance affects the self-insurance-cum-protection level. When the probability of loss is small, the self-insurance-cum-protection and market insurance are substitutes. This means when market insurance is available, people tend to exert less effort on self-insurance-cum-protection.

Suggested Citation

  • Wing Yan Lee & Derrick W. H. Fung, 2021. "Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory," Mathematics, MDPI, vol. 9(22), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2853-:d:676386
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    References listed on IDEAS

    as
    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Doherty, Neil A & Eeckhoudt, Louis, 1995. "Optimal Insurance without Expected Utility: The Dual Theory and the Linearity of Insurance Contracts," Journal of Risk and Uncertainty, Springer, vol. 10(2), pages 157-179, March.
    3. Tim Lohse & Julio R. Robledo & Ulrich Schmidt, 2012. "Self‐Insurance and Self‐Protection as Public Goods," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 57-76, March.
    4. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    5. Dionne, Georges & Eeckhoudt, Louis, 1985. "Self-insurance, self-protection and increased risk aversion," Economics Letters, Elsevier, vol. 17(1-2), pages 39-42.
    6. Kai A. Konrad & Stergios Skaperdas, 1993. "Self-Insurance and Self-Protection: A Nonexpected Utility Analysis," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 18(2), pages 131-146, December.
    7. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    8. McGuire, Martin C & Pratt, John & Zeckhauser, Richard, 1991. "Paying to Improve Your Chances: Gambling or Insurance?," Journal of Risk and Uncertainty, Springer, vol. 4(4), pages 329-338, December.
    9. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    10. Christophe Courbage, 2001. "Self-Insurance, Self-Protection and Market Insurance within the Dual Theory of Choice," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 26(1), pages 43-56, June.
    Full references (including those not matched with items on IDEAS)

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