## Abstract

Choice under risk is modelled using a piecewise linear version of rank-dependent utility. This model can be considered a continuous version of NEO-expected utility (Chateauneuf et al., J Econ Theory 137:538–567, 2007). In a framework of objective probabilities, a preference foundation is given, without requiring a rich structure on the outcome set. The key axiom is called *complementary additivity*.

### Keywords

Rank-dependent utility Security and potential level preferences Optimism Pessimism### JEL Classification

D81## Notes

### Acknowledgments

I am grateful for the comments of an anonymous reviewer. The usual disclaimer applies.

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