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A Note on the Shape of the Probability Weighting Function

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Abstract

The focus of this contribution is on the transformation of objective probability, which in Prospect Theory is commonly referred as probability weighting. Empirical evidence suggests a typical inverse-S shaped function: decision makers tend to overweight small probabilities, and underweight medium and high probabilities; moreover, the probability weighting function is initially concave and then convex. We apply different parametric weighting functions proposed in the literature to the evaluation of derivative contracts and to insurance premium principles.

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References

  1. Abdellaoui, M., L’Haridon, O., Zank, H.: Separating curvature and elevation: a parametric probability weighting function. J. Risk Uncertain. 41, 39–65 (2010)

    Article  Google Scholar 

  2. Davies, G.B., Satchell, S.E.: The behavioural components of risk aversion. J. Math. Psychol. 51, 1–13 (2007)

    Article  MathSciNet  Google Scholar 

  3. Kaluszka, M., Krzeszowiec, M.: Pricing insurance contracts under cumulative prospect theory. Insur. Math. Econ. 50, 159–166 (2012)

    Article  MathSciNet  Google Scholar 

  4. Nardon, M., Pianca, P.: A behavioural approach to the pricing of European options. In: Corazza M., Pizzi C. (eds.) Mathematical and Statistical Methods for Actuarial Sciences and Finance, pp. 217–228. Springer, Milano (2014)

    Google Scholar 

  5. Prelec, D.: The probability weighting function. Econometrica 66, 497–527 (1998)

    Article  MathSciNet  Google Scholar 

  6. Thaler, R.H.: Mental accounting and consumer choice. Mark. Sci. 4, 199–214 (1985)

    Article  Google Scholar 

  7. Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of the uncertainty. J. Risk. Uncertain. 5, 297–323 (1992)

    Article  Google Scholar 

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Correspondence to Martina Nardon .

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Nardon, M., Pianca, P. (2018). A Note on the Shape of the Probability Weighting Function. In: Corazza, M., Durbán, M., Grané, A., Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-89824-7_85

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