Local risk proneness in analytically approximated utility functions under monotonically decreasing preferences

We discuss an analytical arctan form to approximate decreasing utilities based on several nodes of its graphics elicited in interval form. We demonstrate the process on two types of nodes originating from different subjective elicitation approaches. Our focus is also on the local risk attitude estimator, which in the case of decreasing preferences gets interpreted as local risk proneness vs the local risk aversion for increasing preferences.