This paper provides the necessary and sufficient conditions such that economically important individuals, as suggested by Tsetlin et al. (2015), demand a higher coinsurance rate when they face a change in the underlying loss distribution. We further study this issue by classifying the changes in risk into: (1) an increase in the severity of loss, and (2) an increase in the probability of loss. Finally, we provide a numerical example to demonstrate the usefulness of the proposed approach.
