The domain of risk analysis is expanded to consider strategic interactions among multiple participants in the management of extreme risk in a system of systems. These risks are fraught with complexity, ambiguity, and uncertainty, which pose challenges in how participants perceive, understand, and manage risk of extreme events. In the case of extreme events affecting a system of systems, cause-and-effect relationships among initiating events and losses may be difficult to ascertain due to interactions of multiple systems and participants (complexity). Moreover, selection of threats, hazards, and consequences on which to focus may be unclear or contentious to participants within multiple interacting systems (ambiguity). Finally, all types of risk, by definition, involve potential losses due to uncertain events (uncertainty). Therefore, risk analysis of extreme events affecting a system of systems should address complex, ambiguous, and uncertain aspects of extreme risk. To accomplish this, a system of systems engineering methodology for risk analysis is proposed as a general approach to address extreme risk in a system of systems. Our contribution is an integrative and adaptive systems methodology to analyze risk such that strategic interactions among multiple participants are considered. A practical application of the system of systems engineering methodology is demonstrated in part by a case study of a maritime infrastructure system of systems interface, namely, the Straits of Malacca and Singapore.