Biconvex models and algorithms for risk management problems

This paper deals with the risk management problem of determining an optimal mix of available strategies for attenuating accident probabilities as well as the ensuing consequences of harmful events, so as to minimize the total risk associated with a given set of risky activities, subject to budgetary and operational constraints. The problem is modeled as a biconvex programming problem that happens to be nonconvex. For the case of a single risk, the authors propose an outer-linearization scheme that is proven to converge to an optimal solution. By projecting the problem onto the bivariate probability-consequence attenuation space, an alternative graphical solution scheme is also proposed that enables the decision maker to interact subjectively with the process. These models and concepts are extended to the multiple risk situation. Finally, they also provide and discuss alternative models that consider certain strategic issues related to acceptable risk, equitable risk, and the incorporation of uncertainty.