Portfolio Optimization Models for Property-Liability Insurance Companies: An Analysis and Some Extensions

This paper presents a model to assist property-liability insurance companies in making product and investment mix decisions. A quadratic programming approach is used to generate mean-variance efficient frontiers that reflect the covariability of returns on insurance lines and assets. The solution indicates the overall premium-to-surplus ratio, the distribution of premiums among insurance lines, and the proportion of assets in each major investment class that are consistent with the minimum level of risk for a given expected rate of return on net worth. Recognition is given to the tendency for some insurance lines to generate more investable funds than others due to longer lags between claim occurrence and settlement. The importance of federal income taxes in insurance company decision making is recognized, and a method is suggested for including taxes in the model. The traditional model for selecting insurance company operating strategies is safety-first decision making (ruin theory). More recently, utility theory has been suggested as an alternative approach. This paper discusses the linkages between ruin theory and utility theory and indicates how these decision rules can be used to select operating points along the efficient frontier. A numerical example is given based on the published financial data of a major insurance company to illustrate the development of an efficient frontier and the use of ruin and utility-based decision rules. The results indicate that these decision rules generally lead to different operating strategies and that efficiency can be improved using the quadratic programming approach.