The purpose of this paper is to investigate the insights that might be generated into the nature of ' lone wolf terrorism' through the application of economic analysis. Orthodox approaches, particularly (standard) expected utility analysis and game theoretical analysis, are discussed. These tools prove useful in developing preliminary or ' first order' insights. The lone wolf terrorist exhibits a number of idiosyncrasies that present challenges to both economic analysis and government security policy. An alternative analytical framework is constructed wherein a terroristic agent makes choices on the basis of a preference ordering constructed over two moments of the distribution (measured in terms of fatalities generated by terrorist attacks). Seven predictions are yielded from the mean-variance theoretical framework and numerical estimates are computed as preliminary steps towards the full exploration of the implications of the framework. Most importantly, depending on their level of risk aversion (or risk seeking behaviour), lone wolves are expected to predominantly choose assassination, armed attack, bombing, hostage taking or unconventional attacks. Furthermore, within a range of between one and two standard deviations from the mean, it is possible that the quadratic utility function will reach a maximum. Following attacks of a certain magnitude (in terms of fatalities), it might be expected that the lone wolf will withdraw from activity for a period of time. This analytical approach may assist governments and security agencies facing the threat of lone wolf terrorism.