Maritime security assessment is moving towards a proactive risk-based regime. This opens the way for security analysts and managers to explore and exploit flexible and advanced risk modelling and decision-making approaches in maritime transport. In this article, following a review of maritime security risk assessment, a generic quantitative security assessment methodology is developed. Novel mathematical models for security risk analysis and management are outlined and integrated to demonstrate their use in the developed framework. Such approaches may be used to facilitate security risk modelling and decision making in situations where conventional quantitative risk analysis techniques cannot be appropriately applied. Finally, recommendations on further exploitation of advances in risk and uncertainty modelling technology are suggested with respect to maritime security risk quantification and management