Risk management based on probabilistic ATC under uncertainty

This chapter presents a methodology for analytical target cascading (ATC) under uncertainty to address the risk management problem. The proposed hierarchical ATC structure is exactly corresponding to the systematic risk management, which is a multidisciplinary optimization procedure. Since the uncertainty induces risks, the proposed probabilistic algorithm reformulates the ATC method by setting random variables and probabilistic constraints. The proposed ATC method decomposes risk management problem into hierarchical sub-problems, which are linked directly above and below using mean values and standard deviations. With the given risk targets from upper levels transmitting downward, each sub-problem at each level of the hierarchy operates the adaptive optimization method to narrow the gaps between responses and the distributed targets. Once the convergence is attained by iterating between top and bottom, variables and parameters are optimized to reduce the risks. The Risk can be regarded as an optimization target together with efficiency and cost, or it can be contained in constraints in each sub-problem to optimize the efficiency and cost within the prescribed risk boundary. A case of risk management optimization is given to verify the proposed methodology. The results confirm the applicability and efficiency of the probabilistic ATC method under uncertainty in risk management.