Accessibility statement

This paper will be published in the August 2020 issue of the Journal of Risk and Uncertainty.

Some of the material here will appear in the Online Appendix to the published article.

Decisions under Risk: Dispersion and Skewness

Oben Bayrak and John Hey


When people take decisions under risk, it is not only the expected utility that is important, but also the shape of the distribution of utility: clearly the dispersion is important, but also the skewness. For given mean and dispersion, decision-makers treat positively and negatively skewed prospects differently. This paper presents a new behaviourally-inspired model for decision making under risk, incorporating both dispersion and skewness. We run a horse-race of this new model against six other models of decision-making under risk and show that it outperforms many in terms of goodness of fit and shows a reasonable performance in predictive ability. It can incorporate the prominent anomalies of standard theory such as the Allais paradox, the valuation gap, and preference reversals, and also the behavioural patterns observed in experiments that cannot be explained by Rank Dependent Utility Theory.


The paper

Paper (PDF , 1,518kb)


Appendix D:The lotteries used in the experiment

These are the Lotteries (MS Word , 25kb) used in the experiment.


Appendix E: Results with editing (Luce Model)

Appendix E (PDF , 203kb)


Appendix F: Results with and without editing (White Noise)

Appendix F (PDF , 255kb)


Appendix G: The common anomalies found in the literature.

Anomalies (PDF , 94kb).


The various rankings

With the Luce Model: Rankings Version A: RLA_LM (MS Excel , 14kb); Rankings Version B: RLB_LM (MS Excel , 13kb)Rankings Version C: RLC_LM (MS Excel , 12kb).

With White Noise: Rankings Version A: RLA_WN (MS Excel , 13kb) ; Rankings Version B:  .RLB_WN (MS Excel , 13kb); Rankings Version C: 


The GAUSS estimation programs.

The  GAUSS programs (zip , 42kb) can be found here.


The output/results

The output (zip , 685kb)output (zip , 685kb) from the above is here. You can find a Guide to the output (PDF , 260kb) here.