Payoff Kinks in Preferences Over Lotteries

This paper identifies two distinct types of payoff kinks that can be exhibited by preference functions over monetary lotteries - "locally separable" vs. "locally nonseparable" - and illustrates their relationship to the payoff and probability derivatives of such functions. Expected utility and Fréchet differentiable preference functions are found to be incapable of exhibiting locally nonseparable payoff kinks; rank-dependent preference functions are incapable of avoiding them.