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In this paper we present a novel approach of using mathematical models and stochastic simulations to guide and inform security investment and policy change decisions. In particular, we investigate vulnerability management policies, and explore how effective standard patch management and emergency escalation based policies are, and how they can be combined with earlier, pre-patch mitigation measures to reduce the potential exposure window. The paper describes the model we constructed to represent typical vulnerability management processes in large organizations, which captures the external threat environment and the internal security processes and decision points. We also present the results from the experimental simulations, and show how changes in security solutions and policies, such as speeding up patch deployment and investing in early mitigation measures, affect the overall exposure window in terms of the time it takes to reduce the potential risk. We believe that this type of mathematical modelling and simulation-based approach provides a novel and useful way of considering security investment decisions, which is quite distinct from traditional risk analysis.