On Maximizing Profit Through Pricing

Several important practical problems and techniques which are familiar to both actuaries and underwriters are discussed informally and then analyzed mathematically. The main subjects are the degree to which profitability can be improved by estimating the expected losses of risks more accurately, and the usefulness of various methods of improving accuracy. The effect of raising or lowering the general level of insurance rates is also analyzed. The lognormal distribution, the bivariate normal distribution, and some mathematical results relating to prior and posterior distributions are used to produce methods of estimating the value of accuracy, the effects of adverse selection, the value of a "second opinion," and the relation between rate increases or decreases and loss ratios. Mathematical guidelines for using the "stop and go" and "follow the lead" methods of evaluating risks are derived. Several suggestions for research are mentioned at the end, as well as many other places in the paper. Some of the ideas that are used can also be applied to other types of pricing besides property and casualty insurance, such as life insurance and real estate. Two applications to loss reserving are given.