The Role of Risk Measures in Relating Earthquake Risks at Building and Portfolio Levels

The potentially large spatial footprint of earthquake disasters and the increased concentration of population and values in dense urban areas call for an explicit consideration of seismic risk at a regional, building portfolio level. The relation between the building-level seismic risk and the portfolio-level seismic risk is helpful if one wants to meet a specific regional seismic risk tolerance level by specifying seismic risk targets for individual buildings. We examine four types of common risk measures and point to the importance of subadditivity, a risk measure mathematical property, for deriving a conservative upper-bound relation between the building-specific and the building portfolio seismic risks. Subadditive risk measures, such as the Expected Shortfall, allow estimates of conservative upper bounds of the portfolio-level seismic risk. In a case study, we show that nonsubadditive risk measures commonly used in earthquake engineering can lead to counter-intuitive and nonconservative perceptions of the regional seismic risk, especially when one extrapolates from individual buildings to the entire building portfolio. We also illustrate the advantages of subadditive risk measures for regional seismic risk assessment.