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The purpose of this two‐part series is to consider the role of the “scientific method” (SM) in human understanding, questioning both its consistency in actual practice and its reasonableness as a system of philosophy and action.

Part 2 considers problems of inefficiency and inertia caused by the SM's collectivist, frequentist orientation.

It is argued that problems caused by the SM's frequentist framework may be avoided by a more individualist, Bayesian approach.

The two‐part series challenges certain aspects of the “scientific method” as employed in the practice of modern science.

Events surrounding September 11, 2001, have motivated increasing interest in identifying, assessing, and managing the risk of “extreme events.” This article introduces a new mathematical framework for the risk management of extreme event risk. In the article, the author proposes criteria based on “higher” (the third and fourth) moments that dominate variance (the second moment) in explaining the economics of insurance and reinsurance. Economic and financial implications are then applied to the underwriting and investment activities of insurers and reinsurers.

The events of September 11, 2001 have triggered great interest in the identification, assessment, and management of “extreme events.” In this article, we offer a new mathematical framework for the development of financial risk management techniques to address these exposures. Based upon our analysis, we argue that: (1) the decreasing marginal utility of net wealth does not adequately explain the economics of insurance/ reinsurance; and (2) our proposed apprehended value criterion provides approximate justification of mean-third central moment fourth central moment (M-T-F) decision making, thereby “leapfrogging” (skipping over) the variance. Appropriate extensions of traditional financial risk management concepts are then considered, along with their implications for insurer/reinsurer underwriting and investment activity.

The editorial aims to illustrate a major weakness of frequentist estimation – overlooking prior beliefs that are clearly relevant.

A hypothetical forecasting problem is considered in which a law‐enforcement officer has to determine who will be the next victim in a coded sequence constructed by a serial killer. The frequentist method of maximum likelihood is used to select the underlying pattern.

The example shows that it is quite possible for the maximum‐likelihood approach to overlook an intuitively obvious model.

The editorial provides a simple and clear example of the shortcomings of the maximum‐likelihood principle.

The purpose of this paper is to consider the existence and significance of heavy‐tailed – and in particular, infinite‐mean – insurance losses.

Three specific questions are addressed in turn. First, how do infinite‐mean insurance losses arise in the real world? Second, can infinite‐mean losses exist even in the presence of insurance policy limits (caps)? Third, why are infinite‐mean losses so infrequently discussed by practitioners and regulators?

The paper first shows that heavy‐tailed – and in particular, infinite‐mean – insurance losses can be generated by simple modifications of gamma (exponential) random variables. It then finds that the property of infinite means cannot be prevented by the imposition of policy limits (caps). Finally, the paper argues that the statistical contagion and financial intractability of infinite‐mean losses generate a political fear among practitioners and regulators analogous to that associated with a “dread disease.”

The paper explores an important insurance phenomenon – heavy‐tailed/infinite‐mean losses – that is insufficiently discussed.