Risk aggregation considering probabilistic and consequential interactions: A general formulation with computational cost handling

Complicated interaction between risk events is the critical obstacle preventing accurate risk aggregation, which is an important issue in risk management. Recent research integrates interaction into risk aggregation with different perspectives and lacks a comprehensive discussion of this issue, making the risk aggregation process not universal for diverse cases, especially in subjective risk assessment contexts. Therefore, this article proposes a theoretically convincing risk aggregation method embedding different types of interaction to support decision analysis more effectively. The main contributions of this article are as follows: (a) more in-depth and stricter definitions, measures, and graphical descriptions of different types of interaction are developed to ensure the accuracy of risk aggregation; (b) a formal risk aggregation approach that could apply in both objective and subjective risk assessment contexts while elegantly embedding risk interactions is proposed; (c) the additivity of risks and risk sets in the risk aggregation process is discussed in detail and the conditions for additivity are clarified; (d) the quasi-two/three-additive measures, which approximately obtain the aggregate risk value within sufficient reliability, are proposed to greatly reduce the computational cost. To examine the applicability of the proposed general risk aggregation method, a case study is finally presented to show the complete risk aggregation process and its application in the decision-making stage.