Generalised Means of Simple Utility Functions with Risk Aversion
The paper examines the properties of a generalised mean of simple utilities each displaying risk aversion, that is, with first derivative positive and second derivative negative. It proves the mean is itself a valid utility function with the appropriate signs for derivatives and investigates risk aversion properties. It shows that simple component utilities, each of which may have quite restricted risk aversion properties, can be parsimoniously combined through the generalised mean formula to give a much more versatile utility function.
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