Differentiability of von Neumann-Morgenstern utility functions

This paper studies necessary and sufficient preference-based conditions for differentiability of risk averse (prudent, or temperate) von Neumann-Morgenstern utility functions. The very idea to devise those conditions is based on the reverse claim of an old observation by Arrow that a risk-averse expected-utility maximizer will always accept a sufficiently small stake in any positive expected-value bet if her von Neumann-Morgenstern utility function is differentiable.