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Optimal insurance design under narrow framing

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  • Jiakun Zheng

    (Renmin University of China = Université Renmin de Chine, China Financial Policy Research Center - Renmin University of China = Université Renmin de Chine)

Abstract

In this paper, we study insurance decisions when the policyholder evaluates insurance with narrow framing. We show that due to aversion to risk on the net insurance payoff, i.e., insurance indemnity minus insurance premium, narrow framing reduces insurance demand. This helps explaining the observed low insurance demand in many insurance markets. We also show that the optimal insurance contract involves a deductible and the coinsurance of losses above the deductible when transaction costs depend on the actuarial value of the policy. Moreover, when the policyholder is loss averse over the net insurance payoff, a fixed indemnity equal to insurance premium should be paid for a range of intermediate losses.

Suggested Citation

  • Jiakun Zheng, 2020. "Optimal insurance design under narrow framing," Post-Print hal-04227370, HAL.
  • Handle: RePEc:hal:journl:hal-04227370
    DOI: 10.1016/j.jebo.2020.05.020
    Note: View the original document on HAL open archive server: https://hal.science/hal-04227370
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    1. Bond, Eric W. & Crocker, Keith J., 1997. "Hardball and the soft touch: The economics of optimal insurance contracts with costly state verification and endogenous monitoring costs," Journal of Public Economics, Elsevier, vol. 63(2), pages 239-264, January.
    2. Christian Gollier & Alexander Muermann, 2010. "Optimal Choice and Beliefs with Ex Ante Savoring and Ex Post Disappointment," Management Science, INFORMS, vol. 56(8), pages 1272-1284, August.
    3. Barberis, Nicholas & Huang, Ming, 2009. "Preferences with frames: A new utility specification that allows for the framing of risks," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1555-1576, August.
    4. Jeffrey R. Brown & Jeffrey R. Kling & Sendhil Mullainathan & Marian V. Wrobel, 2008. "Why Don’t People Insure Late-Life Consumption? A Framing Explanation of the Under-Annuitization Puzzle," American Economic Review, American Economic Association, vol. 98(2), pages 304-309, May.
    5. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    6. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    7. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    8. Brown, Jeffrey R. & Finkelstein, Amy, 2007. "Why is the market for long-term care insurance so small?," Journal of Public Economics, Elsevier, vol. 91(10), pages 1967-1991, November.
    9. Philip H. Dybvig, 1988. "Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 67-88.
    10. Picard, Pierre, 1996. "Auditing claims in the insurance market with fraud: The credibility issue," Journal of Public Economics, Elsevier, vol. 63(1), pages 27-56, December.
    11. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    12. Lena Giesbert & Susan Steiner & Mirko Bendig, 2011. "Participation in Micro Life Insurance and the Use of Other Financial Services in Ghana," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(1), pages 7-35, March.
    13. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    15. Johnson, Eric J & Hershey, John & Meszaros, Jacqueline & Kunreuther, Howard, 1993. "Framing, Probability Distortions, and Insurance Decisions," Journal of Risk and Uncertainty, Springer, vol. 7(1), pages 35-51, August.
    16. Nicholas Barberis & Ming Huang, 2001. "Mental Accounting, Loss Aversion, and Individual Stock Returns," Journal of Finance, American Finance Association, vol. 56(4), pages 1247-1292, August.
    17. Daniel Kahneman, 2003. "Maps of Bounded Rationality: Psychology for Behavioral Economics," American Economic Review, American Economic Association, vol. 93(5), pages 1449-1475, December.
    18. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    19. Patrick Brockett & Linda Goldens & Min-Ming Wen & Charles Yang, 2009. "Pricing Weather Derivatives Using the Indifference Pricing Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(3), pages 303-315.
    20. Botond Köszegi, 2014. "Behavioral Contract Theory," Journal of Economic Literature, American Economic Association, vol. 52(4), pages 1075-1118, December.
    21. David E. Bell, 1985. "Disappointment in Decision Making Under Uncertainty," Operations Research, INFORMS, vol. 33(1), pages 1-27, February.
    22. Jeffrey R. Brown & Amy Finkelstein, 2011. "Insuring Long-Term Care in the United States," Journal of Economic Perspectives, American Economic Association, vol. 25(4), pages 119-142, Fall.
    23. Carole Bernard & Steven Vanduffel, 2014. "Financial Bounds for Insurance Claims," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(1), pages 27-56, March.
    24. Daniel Kahneman & Dan Lovallo, 1993. "Timid Choices and Bold Forecasts: A Cognitive Perspective on Risk Taking," Management Science, INFORMS, vol. 39(1), pages 17-31, January.
    25. Mohammed Abdellaoui & Han Bleichrodt & Corina Paraschiv, 2007. "Loss Aversion Under Prospect Theory: A Parameter-Free Measurement," Management Science, INFORMS, vol. 53(10), pages 1659-1674, October.
    26. Jeffrey R. Brown, 2007. "Rational and Behavioral Perspectives on the Role of Annuities in Retirement Planning," NBER Working Papers 13537, National Bureau of Economic Research, Inc.
    27. Jeffrey R. Brown & Arie Kapteyn & Olivia S. Mitchell, 2011. "Framing Effects and Expected Social Security Claiming Behavior," NBER Working Papers 17018, National Bureau of Economic Research, Inc.
    28. Louis Eeckhoudt & Anna Fiori & Emanuela Rosazza Gianin, 2018. "Risk Aversion, Loss Aversion, and the Demand for Insurance," Post-Print hal-02987006, HAL.
    29. Jeffrey R. Brown & Arie Kapteyn & Olivia S. Mitchell, 2011. "Framing Effects and Expected Social Security Claiming Behavior," NBER Working Papers 17018, National Bureau of Economic Research, Inc.
    30. Segal, Uzi & Spivak, Avia, 1990. "First order versus second order risk aversion," Journal of Economic Theory, Elsevier, vol. 51(1), pages 111-125, June.
    31. Nicholas Barberis & Ming Huang, 2001. "Mental Accounting, Loss Aversion, and Individual Stock Returns," NBER Working Papers 8190, National Bureau of Economic Research, Inc.
    32. Louis Eeckhoudt & Anna Maria Fiori & Emanuela Rosazza Gianin, 2018. "Risk Aversion, Loss Aversion, and the Demand for Insurance," Risks, MDPI, vol. 6(2), pages 1-19, May.
    33. Michael Braun & Alexander Muermann, 2004. "The Impact of Regret on the Demand for Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(4), pages 737-767, December.
    34. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    35. Keith J. Crocker & John Morgan, 1998. "Is Honesty the Best Policy? Curtailing Insurance Fraud through Optimal Incentive Contracts," Journal of Political Economy, University of Chicago Press, vol. 106(2), pages 355-375, April.
    36. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    37. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.
    38. Justin Sydnor, 2010. "(Over)insuring Modest Risks," American Economic Journal: Applied Economics, American Economic Association, vol. 2(4), pages 177-199, October.
    39. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
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    Cited by:

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    2. Tim J. Boonen & Xia Han, 2023. "Optimal insurance with mean-deviation measures," Papers 2312.01813, arXiv.org.

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