Multi-risk approaches have been recently proposed to assess and compare different risks in the same target area. The key points of multi-risk assessment are the development of homogeneous risk definitions and the treatment of risk interaction. The lack of treatment of interaction may lead to significant biases and thus to erroneous risk hierarchization, which is one of primary output of risk assessments for decision makers. In this paper, a formal statistical model is developed to treat interaction between two different hazardous phenomena in long-term multi-risk assessments, accounting for possible effects of interaction at hazard, vulnerability and exposure levels. The applicability of the methodology is demonstrated through two illustrative examples, dealing with the influence of (1) volcanic ash in seismic risk and (2) local earthquakes in tsunami risk. In these applications, the bias in single-risk estimation induced by the assumption of independence among risks is explicitly assessed. An extensive application of this methodology at regional and sub-regional scale would allow to identify when and where a given interaction has significant effects in long-term risk assessments, and thus, it should be considered in multi-risk analyses and risks hierarchization.
