The Impact of Risk Aversion on the Rigidity of Insurance Premiums

A risk averse insurance company which knows the quota of coverage demanded by a client at the status-quo premium but has imperfect information otherwise may choose not to change the premium although an else identical risk neutral company would do so, provided the variance of the company's subjective probability distribution over the quota demanded as a function of the premium displays a kink at the status quo. This is equivalent to risk aversion of order 1. When no such fixed premiums exist, the size of premium adjustment still decreases substantially as risk aversion increases. Moreover, in case of small premium adjustment costs increasing risk aversion significantly diminishes the size of costs sufficient to keep the premium unchanged.