Risk Management and the Theory of the Firm

Abstract

This article integrates risk management decision variables into the theory of the firm under risk and develops risk management decision rules consistent with the firm's overall objectives. The theoretical construct chosen for extension to the risk management problem is the capital asset pricing model. Utilizing this model, decision rules are developed for optimal proportional retention, selection of aggregate deductibles and choosing reserving policies. The results differ significantly from the expected value decision rules developed by previous researchers. The article concludes by examining the impact on the decision rules of relaxing some of the key assumptions of the model. Recent years have witnessed significant progress in the application of quantitative decision tools to the solution of risk management problems. These developments have ranged from purely theoretical exercises to highly particularized practical applications and have encompassed the entire spectrum of quantitative methodology. For example, a model for the selection of optimal deductibles has been developed and applied by Allen and Duvall [1, 4]. Optimal insurance and loss prevention decisions have been the subject of a paper by Shpilberg and de Neufville [16] which employed a decision theoretic framework. A study which involved the testing of alternative decision tools, such as utility theory and the worry factor method, has been conducted by Neter and Williams [13] while a computer simulation model of self insurance of workers' compensation losses was developed by Mortimer [11]. The fitting of loss distributions to facilitate the more precise estimation of future claim costs has been emphasized by Hartman and Siskin [9]. Finally, Head [8] has illustrated how capital budgeting can be applied in the context of risk management decision making. These and numerous other studies have provided the basis for significant improvements in risk management analysis. However, as is perhaps inevitable in a developing field, most of the articles have concentrated on J. David Cummins is Assistant Professor of Insurance in the Wharton School, University of Pennsylvania. Professor Cummins is Research Director of the S. S. Huebner Foundation and is a member of the Editorial Board of the Journal of Risk and Insurance. He is the author of An Econometric Model of the Life Insurance Sector of the U.S. Economy and co-author of Consumer Attitudes Toward Auto and Homeowners Insurance. This paper was submitted for publication June, 1975. It was presented to the 1975 Risk Theory Seminar.