A mathematical perspective on the formalization of risk mitigation

The classic definition of risk as the product of hazard, exposure and vulnerability was initially intended as a qualitative rather than quantitative formula. Its informal nature becomes more apparent when evaluating strategies for risk mitigation, for which different informal equations have been presented in the literature.

We offer here a mathematical perspective on the equations that define risk and a novel approach for a quantitative analysis of risk mitigation that help highlight decision variables among the many input variables that participate in risk analysis and modeling.

We show how the classic Risk = Hazard * Exposure * Vulnerability formula represents a zero-order approximation of the more formal integral representation that we derive, and that risk mitigation can be quantified based on parallels with mathematical homotopies with an associated cost function, with an interesting outlook on the design of both long-term and short-term risk mitigation strategies.