Insurance versus Self-Insurance: A Risk Management Perspective

The scientific risk-retention or self-insurance decision from a utility theoretic point of view is examined under the assumption that the risk manager has only partial stochastic information about the loss severity distribution. When only the range and a few central moments are known about the loss severity distribution, it is shown how to obtain maximally tight bounds on the expected utility of self insurance. Significantly, the extremal probability distributions derived do not depend upon the particular decision maker's utility function and, therefore, should be applicable to a wide variety of financial decisions. Moreover, financial and/or risk managers in a business can make decisions without assessing the preference structure of the firm's owners.