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Insurance and Probability Weighting Functions


  • Ali al-Nowaihi


  • Sanjit Dhami



Evidence shows that (i) people overweight low probabilities and underweight high probabilities, but (ii) ignore events of extremely low probability and treat extremely high probability events as certain. Decision models, such as rank dependent utility (RDU) and cumulative prospect theory (CP), use probability weighting functions. Existing probability weighting functions incorporate (i) but not (ii). Our contribution is threefold. First, we show that this would lead people, even in the presence of fixed costs and actuarially unfair premiums, to insure fully against losses of sufficiently low probability. This is contrary to the evidence. Second, we introduce a new class of probability weighting functions, which we call higher order Prelec probability weighting functions, that incorporate (i) and (ii). Third, we show that if RDU or CP are combined with our new probability weighting function, then a decision maker will not buy insurance against a loss of sufficiently low probability; in agreement with the evidence. We also show that our weighting function solves the St. Petersburg paradox that reemerges under RDU and CP.

Suggested Citation

  • Ali al-Nowaihi & Sanjit Dhami, 2005. "Insurance and Probability Weighting Functions," Discussion Papers in Economics 05/19, Department of Economics, University of Leicester, revised Sep 2006.
  • Handle: RePEc:lec:leecon:05/19

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    References listed on IDEAS

    1. Ali al-Nowaihi & Sanjit Dhami, 2010. "Probability Weighting Functions," Discussion Papers in Economics 10/10, Department of Economics, University of Leicester.
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    Blog mentions

    As found by, the blog aggregator for Economics research:
    1. Is insurance irrational?
      by chris dillow in Stumbling and Mumbling on 2006-04-22 18:49:45


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    Cited by:

    1. Sanjit Dhami & Ali al-Nowaihi, 2006. "Hang ’em with probability zero: Why does it not work?," Discussion Papers in Economics 06/14, Department of Economics, University of Leicester.
    2. Ali al-Nowaihi & Ian Bradley & Sanjit Dhami, 2006. "The Utility Function Under Prospect Theory," Discussion Papers in Economics 06/15, Department of Economics, University of Leicester.

    More about this item


    Decision making under risk; Prelec’s probability weighting function; Higher order Prelec probability weighting functions; Behavioral economics; Rank dependent utility theory; Prospect theory; Insurance; St. Petersburg paradox;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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